Conceptual Design Report: Electric Powered Tricycle

ME 329-10

Spring 2017

June 6, 2017

HERMES

Caleb Barnett Nathan Hoyt

Matthew Callaghan Ryan Meinhardt

River Drake Alex Shaw

Cullen Goss Paul Song

Instructor:

Professor John Fabijanic

Mechanical Engineering Department

California Polytechnic State University

San Luis Obispo

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System Summary Sheet 3 Executive Summary 4 Problem Definition 6

Problem Statement 6 Background Information 6 Design Requirements 7 “Normal” Conditions Definition 9 Trail Conditions 9 Rider Conditions 10

Development Process 11 Differential Decision Matrix 11 Power Transfer Decision Matrix 13 Tadpole Versus Delta 16 Framing 17 User Interface Decision Matrices 18

Detailed Design Description 23 Powertrain Subsystems 27

Dimensions 27 System Analysis 29

Powertrain Efficiency 29 Chains 29 Differential 31 Cassette Shaft 32 Front Axle Design 33 Bearing Selection 34 Cost 35

Improvements on Initial Design 36 Conclusion 36 References 38 Appendices 40

A. Detail drawing of full CAD model of trike 40 B. System Trade Study Tools and Results 41 C. Sample Calculation for Chain 46 D. Sample Calculation for Shafts 48 E. Sample Calculation for Bearings 51 F. Sample Calculation for Torque Splitting 52 G. Sample Calculation for Bevel Gears 55

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System Summary Sheet

Tricycle configuration: Tadpole Weight Geometry Total (kg.) 157 Wheelbase (m) 1.45

Rider (kg.) 100 Track (m) 1.3

Structure (kg.) 21.9 Seatback Angle (deg.) 55 but it is adjustable

Motor (kg.) 4.80 C.G. Pos.

Battery (kg.) 12.0 Height (m) 0.630

Transmission (kg.) 12.0 b (m)* 1.01

Driveshaft Assy (kg.) 3.00 Weight Dist. w/ rider

(%F/%R) 70%/30%

Wheels and tires (kg.) 3.30

Drivetrain Weight (kg.) 29.7 What wheels were driven?

Give a short description of your drivetrain concept.

FWD (0, 1 or 2)

Efficiency 90% RWD (0, 1 or 2) 2

ξfinal 1.55, 1.21,1, 0.85, 0.53 Under what conditions? 1

Under what conditions? Under all conditions

Components Tires (type) Continental Trail King MTB Tyre on 650b Mavic MTB wheels

Diameter (m) 0.70

Cr 0.01

Battery Pack 48V 30Ah V5 LiFePO448V

Capacity (Ah) 30Ah

* position of c.g. ahead of rear axle

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Executive Summary

The goal of HERMES is to provide a trike to disabled people who have a sense of adventure

but not necessarily the strength to explore the outdoors on their own. It is designed so that it can

traverse both well-maintained and poorly maintained trails. Ideally, the trike is meant to be used

alongside non-disabled persons, either walking or riding mountain bikes, to ensure that the user has

support in the event of an emergency. The trike was designed so that the user could have confidence

in its safety and durability in the case of tip-over or more extreme terrain. Specific parts were chosen

so that the user could perform maintenance on the trike with ease due to the use of off-the-shelf

mountain bike parts. The need for a trike like HERMES is important because many disabled

persons do not have the strength to pedal a hand-crank style trike. Many of these trikes are also hard

to maintain for the average user while HERMES is designed to be easy and inexpensive to repair.

HERMES was designed to provide a way for those with limited use of their limbs to join their

friends and family on outdoor experiences. HERMES will be considered an Off-Highway Vehicle

(OHV) under United States Forest Service (USFS) regulations and must be registered. Registration

of the vehicle will be the responsibility of the owner and will depend on the owner’s state of

residence.

Figure 1. Total system design in simulated environment.

An isometric view of the final design can be seen above in Figure 1. The trike runs on a

Bafang MMG32 DC motor and Ping 48V V5 LiFePO4 30 Ah battery. It has a maximum range of

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135.185km (84mi) at a speed of 16.09kmh (10mph). The motor is positioned underneath the rider's

knees to maximize ground clearance and in addition, its cover will act as leg supports. This allows

the user to travel at speeds up to 40.23kmh (25mph), which is reasonable considering a fit bicyclist

can travel about 32.19kmh (20mph) on a flat stretch. The trike is also capable of climbing hills up to

a 38% grade. The wheels are 650b mountain bike wheels, which are a standard size for ease of

replacement. Their size also makes it easier to clear large obstacles in the case of a poorly maintained

trail. The trike has a ground clearance of 180mm (7.087in).

The motor attaches to a cassette with multiple sprockets, which will allow the trike to

operate at its highest efficiency depending on what the user demands, whether that be climbing a

grade or speeding down a flat stretch of trail. The gear ratios available on the cassette range from

0.53 to 1.55. The differential, located on the front axle, serves to minimize stresses in the shaft and

provides the user a more comfortable experience. The seat back angle can range from 55 – 70

degrees because each rider will be comfortable in a different position and will require varying

visibility depending on the incline of the trail. The track width of the trike is 1.3m (4.265ft) and the

length is 1.45m (4.757ft). The total mass of the trike, excluding than the rider, is 57.0kg (125.6lb).

The center of gravity is at 0.63m (2.067ft) high, 1.01m (3.313ft) from the rear shaft, and along the

center of the frame. The weight distribution is 50/50 from left to right and 70/30 front to back to

ensure the trike is stable and not prone to tip-over.

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Problem Definition

Problem Statement

HERMES will be a battery-powered recreational off-road trike that will provide a

handicapped rider with the ability to traverse safely and comfortably on off-road terrain in a quick

and efficient manner, giving the rider the ability to accompany groups of non-disabled hikers or

mountain bike riders. It will need to accommodate adult users with a varied selection of below waist

disabilities as described below, while maintaining safe and secure riding conditions. HERMES will

also need to be easily customized and maintained. In addition, it needs to be both compatible with

common mountain bike parts and no more complex to disassemble and reassemble than a typical

bike.

Background Information

The client requirements were adjusted and more detail was added to have a clearer picture of

what the vehicle should be capable of. Research was performed to better understand different types

of disabilities and what the trike should accommodate. Although there are many disabilities that

include the inability to use one or both arms, the trike is designed only for those who can use both.

With that severe of a disability, it would be difficult for the rider to steer and safely control the

motorized trike at the desired speeds or over rough terrain. The trike is designed to be able to access

trails maintained to Road Maintenance Level 2, as defined by the USFS. Level 2 trails are defined as

single-lane roads, cleared of debris but with an unmodified surface [1]. The trike design is focused

on reliability and maintainability in mind instead of performance. The goal was to make an off-road

trike that was robust enough to withstand more rugged terrain than merely 'normal conditions' but

was also accessible enough to replace broken parts.

Research on previous off-road trike designs began to set expectations for the size, weight,

and orientation of the drivetrain. To position the rider, anthropomorphic data was used to

accommodate the 99th percentile of riders. The seat was designed using thigh girth and hip width

measurements. The rest of the seat was designed around the average height of an adult male. The

steering column was placed within reach of riders with arms within the 99th percentile of adult males.

All anthropomorphic data was found in the ASTM Standard Tables of Body Measurements for

Mature Men [2]. In preliminary research, it was found the tadpole design is by far the most

prevalent, further discussed in "Development Process". Previous designs also provided reasonable

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starting points for seat angles, total length, and track. Ranges of these values can be seen in Table 1

below.

Table 1. Dimensions of existing off-road trikes

Parameter Range

Seat Angle 25-70°

Length 1.7 – 2.1m (5.578 - 6.890ft)

Track 0.70 – 0.83m (2.297 - 2.723ft)

Ultimately, the product requirement for HERMES required a deviation from these

established ranges to accommodate tipping and placement of drivetrain, which will be discussed in

“Development Process”.

The only existing model with provided information on turning angle is the Bomber RS Off-

road tricycle. This trike has a maximum turning angle of 60° [3]. This angle became the goal, as it

would allow for HERMES to make a 180 degree turn while remaining on the trail it is designed for.

In addition, prices of current off-road trikes were researched to give a general guideline as to

what cost for HERMES would be reasonable. Existing models ranged anywhere from $4449 for the

Ivacare Top End Force CC [4] to $7400 for the Bomber Offroad Recumbent Handcycle [3]. A base

model electric trike by Horizon costs $13000, but has a larger battery and motor than required for

HERMES [5]. HERMES should be expected to cost somewhere between the high-end handcycle

and the higher performance electric trike.

Design Requirements:

Vehicle has 3 wheels, with only two being coaxial.

All wheels on the vehicle are motor driven.

Under low grip conditions, at least one front and one rear wheel must be powered.

Riding/sitting position is to be nominally upright, with a ride angle range of 55 degrees to 70

degrees from horizontal.

The vehicle riding seat should accommodate riders at the 95th percentile of both male and

females using the 1988 U.S. Army Anthropometry survey (ANSUR) and ASTM documents,

D6240/D6240M (standard tables from adult males) & D5585 (standard tables for adult

females) [2].

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Must use one Bafang MMG32 motor.

Must use only one Ping 48V V5 LiFePO4 battery pack, with a capacity of 10, 15, 20, 25, or

30Ah, operating within conditions detailed in the manufacture specifications documentation.

All components, especially electronics, should be safe to operate in inclement weather (i.e.

heavy rain, light snow).

Must use a common size of mountain bike wheels/tires to reduce maintenance cost.

Must use standard mountain bike parts where possible, including but not limited to:

o Tensioners

o Chains

o Brakes

o Derailleurs

Top speed must be at least 24.14kmh (15mph), under “normal conditions” (see "'Normal'

Conditions Definition" below).

Minimum range must be at least 32.19km (20mi), under the specified “normal conditions”.

Must be able to drive up a 14° incline, with all other conditions being normal.

Must be able to drive laterally across a 45° incline without tipping sideways.

Must be able to support adult riders up to 100kg (220lb).

Must have a turning radius no more than 2m (6.5ft).

Must be able to negotiate a National Forest Service Maintenance Level 2 Road [1].

o Single lane

o No shoulders

o Limited sight distance due to vegetative encroachment

o Has a native surface: no resurfacing or leveling of trail has been done

Must be able to be used by a person with bilateral hip disarticulation or any lesser lower

body disability and use of both arms.

Primary components must be easily disassembled using tools used to maintain any other

mountain bike.

Must be able to brake to a complete stop from full speed in less than 50ft under “normal

conditions” (see "'Normal' Conditions Definition" below).

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Must have a frame and mechanical lifetime comparable to other common mountain bikes

(Not including electronics).

o Under moderate weekly use on the trail standard we defined, the expected frame life

for an aluminum mountain bike is 35,000 km [6].

Must have a total weight of no more than 90kg (198.42lbs) maximum not including rider

(Goal weight <45kg (>99.21lbs)).

Rider seat restraints:

Must retain the rider in the riding position always, even in event of tipping.

Must be able to be removed under the rider's own power for safety reasons.

Must allow for removal at awkward angles such as during full tip over of the vehicle.

May be adjusted or changed to fit different body sizes, based on adult male and

female 95th percentiles from the 1988 U.S. Army Anthropometry survey (ANSUR)

and from ASTM documents, D6240/D6240M (standard tables from adult males) &

D5585 (standard tables for adult females) [2].

'Normal' Conditions Definition:

Conditions under which performance aspects of the trike are measured.

Environmental Conditions:

No inclement weather.

No head or tail winds. Wind resistance is only due to the motion of the vehicle.

Ambient temperature falls within the optimal operating temperatures of the motor and

battery.

o Battery: -20C to +70C (-4F to 150F) [7]

o Bafang Motor: -20C to 55C (-4F to 131F) [8]

Trail Conditions:

Trail is made of dirt, with coefficients for grip of dirt provided.

Trail is flat

Trail does not have any debris or large bumps on the surface

Trail is straight

Trail is wide enough for the vehicle to drive on

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Figure 2. An example of an appropriate riding trail from USFS trail maintenance guide [1].

Rider Conditions:

Rider meets the sizing requirements to fit safely within the restraints

Rider meets the physical riding requirements (defined above)

Rider is an adult weighing approx. 80kg (180lbs)

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Development Process

Differential Decision Matrix:

The characteristics chosen to evaluate the merit for whether to have a differential or not are as

follows:

Efficiency (E): Evaluates the losses due to slipping and friction of the differential gears

Weight (W): How much the configuration weighs in contrast to the other options

Cost (C): This category describes upfront cost but not maintenance cost

Reliability (R): This category deals with the stresses in the drive shaft because of the slippage

at the wheels or the gears in the differential.

Performance (P): This category describes how well the configuration performs with its

traction and turning capabilities.

These qualities were then ranked by comparing their importance to the trike as shown in Table

2. The rankings were then used to assign point values for scoring different designs. The results

are scored in Table 3.

Table 2. Summarization of desired differential characteristics compared against each other.

Comparison Chosen

Characteristic

E vs. W W

E vs. C C

E vs. R R

E vs. P P

W vs. C C

W vs. R W

W vs. P P

C vs. R C

C vs. P P

R vs. P P

Total Values = 10; normalization factor = 1/10

0E + 2W + 3C + 1R + 4P = 10

0.5 was added to E to bring the normalization factor to 10.5.

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Table 3. Decision matrix with the purpose of assessing the necessity of a differential.

Criteria Weighted No Differential Differential

Efficiency 0.05 1 0

Weight 0.19 1 0

Cost 0.29 1 0

Reliability 0.10 0 1

Performance 0.38 -1 1

Sum 1 0.14 0.48

Additional Reasoning:

Efficiency: Not having a differential means that the power from the main drive train is

transferred directly to the wheels instead of having to go through a set of gears which would

inevitably lose some of that power in friction.

Weight: Having a differential would add weight to the body of the design, although without

a differential the shaft would need to be thicker to be able to support higher stresses. It was

decided that the added weight of the differential would be greater than the added weight of a

larger shaft diameter.

Cost: Similarly, in this category, adding a differential adds quite a bit of upfront cost, usually

somewhere around $400.

Reliability: Without a differential, the stresses in the shaft will be greatly increased since one

wheel must slip to turn and depending on the surface, that could be difficult to accomplish.

The differential not only reduces the stresses caused by the need to slip, but also splits the

shaft in half which helps with deflection and the large bending stresses and issues with

critical speed that are seen in long shafts.

Performance: Without a doubt, the differential configuration does much better this category.

This is because a differential allows the wheels to turn at different speeds which makes

turning smoother and easier.

Using the table values and reasoning, it was decided that using a differential would be more

advantageous to the overall usability of the design. The differential that HERMES will use can

be seen in the CAD drawing in Figure 3 below.

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Figure 3. Differential of HERMES. Has a ring “sprocket” instead of the typical gear.

Power Transfer Decision Matrix:

The characteristics chosen to be used to evaluate the merit for different methods of power

transmission are as follows:

Efficiency (E): This category deals with the losses due to slipping or friction of the gears

Cost (C): This category describes upfront cost and not maintenance cost

Weight (W): How much the configuration weighs in contrast to the other options

Reliability (R): This category deals with how often the configuration needs to be maintained

Adaptability (A): This category describes how adaptive the system is to going over large

rocks and rougher terrain

Complexity (X): This category deals with how easy it is to maintain the system

These qualities were then ranked by comparing their importance to the trike as shown in Table 4.

The rankings were then used to assign point values for scoring different drivetrain designs. The

results are scored in Table 5.

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Table 4. Summarization of desired drivetrain characteristics compared against each other.

Comparison Chosen

Characteristic

E vs. C C

E vs. W W

E vs. R R

E vs. X X

E vs. A A

C vs. W C

C vs. R C

C vs. A C

C vs. X X

W vs. R W

W vs. A W

W vs. X X

R vs. A A

R vs. X X

A vs. X A

Total Values = 14; normalization factor = 1/14

0E + 4C + 3W + 1R + 3A + 3X = 14

0.5 was added to E to bring the normalization factor to 14.5.

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Table 5. Decision matrix with the purpose of assessing the most ideal method of power

transmission.

Criteria Weighted Sprockets/Chains Gears/Shafts Belts

Efficiency 0.03 0 1 -1

Cost 0.28 1 0 1

Weight 0.21 0 -1 1

Reliability 0.07 0 1 -1

Adaptability 0.21 1 -1 1

Complexity 0.21 1 -1 0

Sum: 1 0.69 -0.52 0.59

Additional Reasoning:

Efficiency: In this category, belts were ranked last because we are concerned they would slip.

Gears and shafts were ranked best because you would minimize losses in the chains if

instead there was one long drive shaft.

Cost: Upfront cost was more based upon material costs which is why gears and shafts didn't

do as well in this category. They are solid pieces of metal which are costly to manufacture.

Belts and chains do not have this problem and are usually easy to find off the shelf.

Weight: Gears and shafts weight a lot more than chains and belts because of their solid metal

design. Belts are plastic and weigh much less, and chains, although made of metal, are also

lighter than their shaft and gear counterparts.

Reliability: Belts would have to be replaced quite often in comparison to chains which

usually should be replaced every two years or so. Shafts and gears would almost never need

to be replaced unless they were severely damaged in some sort of accident.

Adaptability: Having a long drive shaft that travels the length of the trike would be

dangerous in terms of clearance. If the driver attempted to travel over a large obstacle and in

the process bent the shaft, the trike would not function. Both chains and belts allow for

higher deflection because of their flexible shape.

Complexity: Shafts and gears are very difficult to replace if bent or broken. Belts require

additional design to provide a way to take them on and off their gears. Chains are by far the

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easiest to replace given their pin and hole design and can be simply removed from their

sprockets and replaced using a chain breaker.

Comparing the scores between the 3 different configurations, it was clear that the best method of

power transfer is sprockets and chains.

Tadpole Versus Delta:

A tadpole-style trike was chosen for its more reliable steering and to avoid loss of control in

a sharp turn at higher speeds. Figure 4 below compares the shape and steering of delta and tadpole

trikes. The tadpole design puts more weight over the front wheels, so in a sharp turn the lateral

acceleration will cause understeer which is much easier to control and correct than oversteer which

would occur in the same scenario with most of the weight over the rear, which is the case of the

delta configuration [9]. Braking is primarily done with the front wheels [9], giving the tadpole design

an advantage with two front wheels. Delta designs commonly experience an issue called “nose

diving” where a small imbalance causes the vehicle to roll onto its side while braking [9]. Due to the

design requirement that both the front and rear axles be powered, the delta configuration suffers a

disadvantage compared to the tadpole in steering. The delta configuration would require a more

complex power transfer method than the tadpole as chains would not be able to bend with the front

wheel as it turns. The tadpole design mitigates this issue as the front axle can be driven

independently of the steering mechanism. Due to these advantages, the tadpole configuration was

chosen as the superior design.

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Figure 4. A visual comparison of steering for tadpole and delta tricycle configurations [9].

Framing:

Frame design began with researching other off-road trike designs. Most frames consisted of

aluminum tube stock welded in a T-shape. A basic shape was created using anthropomorphic data to

develop initial dimensions for length, track, and seat position. The initial design of the frame on

SolidWorks looks quite different from the final design. The initial design can be seen below in

Figure 5.

Figure 5. Isometric view of initial design.

Besides giving the project some initial direction, this design was quickly abandoned. The

square shape and lack of triangular trusses made it bulky and not structurally sound. It had a

clearance of 245mm (9.646in) which would have made the center of gravity too high to avoid

transverse tipping within a reasonable range of lengths and tracks. A new design was created by

superimposing the component assembly on the frame and altering the dimensions to fit the

drivetrain. An iterative process was then used with a MATLAB script to determine length and track

dimensions to meet the tip-over requirements, as well as an acceptable turning radius. For tipping,

the goal was to make sure all wheels would have some normal force exerted on them at the

maximum lateral transverse condition of 45 degrees. With tipping being the main concern, the track

and length were designed to be a minimum to meet this requirement because excess length and track

would provide unnecessary extra stability while reducing maneuverability.

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Tip-over criteria were checked at every dimension between track measurements of 0.5m

(1.64ft) and 3m (9.843ft) and wheelbases of 0.62m (2.034ft) and 4.0m (13.123ft). A plot was

generated showing the weight on the uphill wheel while traversing a 45-degree incline, where a force

below 0N on the uphill wheel means the trike will tip during the traverse. Acceptable dimensions are

highlighted in green. The plot, Figure 6, was generated by holding all components the same distance

from the front axle and holding the center of gravity height constant.

Figure 6. Plot of force on uphill wheel during traverse. Green region shows acceptable dimensions.

Additionally, suspension was neglected because the inclusion would create far more

problems for the design than the added comfort it would give the rider. Suspension is difficult to

integrate, creates a need for vibrational analysis, and causes the frame to shift. The last of these

issues is the most problematic because it would cause the drivetrain to shift, which would cause

chain slippage and components to wear out more quickly.

User Interface Decision Matrices:

The following were criteria definitions used to determine which systems for braking,

steering, shifting and throttling were most acceptable based on the design requirements.

Precision: This factor considers road feedback and how easily the user can control and

maneuver the trike the way they want. This is important for the safety of the user.

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Cost: Lowering the cost would make it easier for consumers to buy and for manufacturers to

produce. Usually the lower the cost, the easier it is to manufacture.

Accessibility: The user should have easy access to each of the controls. This factor also

considers the physical demand of the mechanism.

Complexity: Simple mechanisms can be analyzed and modeled easier. Usually cost and

complexity of the mechanism goes hand-in-hand.

Flexibility: This factor considers the amount of orientations and placements possible for a

specific mechanism. This is important because flexibility determines the compatibility

between the different subsystems.

For both the braking and steering subsystems, the importance of each factor to the subsystem was

determined. A weight was then assigned to that criteria, shown in Table 6, 8 and 10. These

weightings were then used to create the decision matrices: Table 7, 9, and 11.

Braking:

Table 6. Weight factors of characteristics to decide braking system

Factor Weight (1-3)

Precision 3

Cost 2

Accessibility 2

Complexity 3

Flexibility 2

Table 7. Decision matrix for braking system

Idea Precision Cost Accessibility Complexity Flexibility of Design

Weighted Total Scores

Road Bike 4 3 4 4 4 46

Mountain Bike

4 3 4 3 3 41

Buttons 1 2 5 2 4 31

Lever 5 4 3 4 2 45

The biggest factors to consider when selecting a braking system are precision and simplicity of

design. Braking systems must allow for variable input to brake safely which eliminates buttons as

one of the potential options. Levers would provide the most precision, but are less accessible to the

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user with limited physical abilities and are not as flexible of a design. A road bike brake system, in

which the rider pulls a small vertical lever on the steering mechanism to engage the brakes, was

chosen for the design because it integrates with the shifting mechanism and rest of the steering

column smoothly. This system will be used to activate the trike’s disk brakes.

Steering:

Table 8. Weight factors of characteristics to decide steering system

Factor Weight (1-3)

Precision 3

Cost 2

Accessibility 2

Complexity 3

Flexibility 2

Table 9. Decision matrix for steering system

Idea Precision Cost Accessibility Complexity Flexibility of

Design Weighted

Total Scores

Handlebars 4 4 3 4 4 46

Steering Wheel

5 3 4 4 4 49

Joystick 3 3 5 3 3 40

Game Controller

2 3 2 2 2 26

Levers 4 5 3 4 3 46

For steering, precision and simplicity of design were weighted higher than the other factors.

The user must be able to steer precisely for a safe ride and must also have road feedback, which

joysticks and game controllers lacked. The design must be simple to reduce maintenance required.

The decision came down to bicycle handlebars, steering wheel, and steering levers. Ease of

accessibility made a steering wheel a better choice than handlebars and levers because the physical

demands of a steering wheel were lower. Upon working on the decision matrix, another idea was

created by combining the handlebars and steering wheel into an airplane-style pilot wheel. This

design was chosen for the steering component because it would have less physical demand, would

be intuitive to use, have easy access to braking, throttling, and shifting, and would yield easier

maneuverability.

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Throttle:

Table 10. Weight factors of characteristics to decide throttle design.

Factor Weight (1-3)

Precision 3

Cost 1

Accessibility 2

Complexity 2

Flexibility 3

Table 11. Decision matrix for throttle design.

Idea Precision Cost Accessibility Complexity Flexibility

of Design

Weighted total

Scores

Motorcycle 5 3 3 3 3 39

ATV 4 4 4 3 4 42

Buttons 1 5 3 4 4 34

Incremental Lever

2 4 4 3 2 30

For throttling, precision was weighed higher for the same reason as steering. Buttons do not

provide road feedback and incremental levers are not as safe of an option because of its positioning.

The motorcycle-style throttle would provide the highest precision, however it did not do as well in

the flexibility category. Bearing in mind that the user might not have legs, the placement of the

throttle needs to be near or attached to the steering mechanism. Since the motorcycle-style throttle

must be on a handlebar, the option did not seem feasible with the other steering options. The best

choice is an ATV-style throttle because it is as precise as a motorcycle-style throttle and is flexible

enough to work with the steering design chosen.

Shifting:

Shifting was deemed necessary even though it was not a design requirement. Shifting and

different gear ratios helps to put less strain on the motor and lengthen its life. Shifting can allow the

trike to stay near the maximum efficiency of the motor while still performing at higher speeds and

torques. The shifting method chosen was a road bike style because it is simple to integrate with the

braking system as seen in Figure 7. The small lever releases cable to shift to a smaller sprocket; the

large lever pulls cable to shift to a larger sprocket.

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Figure 7. Example of road bike style shifter

In conjunction with shifting, an assumption was made that the current draw of the motor

would be controlled intelligently. An intelligent motor control system would be required to

maximize the output of the motor, but for the purposes of this project, how the motor output is

controlled is irrelevant and simply works.

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Detailed Design Description

The drivetrain was designed with simplicity and accessibility in mind. The motor is located

underneath the rider's knees to ensure that the drive train is positioned high enough that clearance

isn't an issue. The 46-tooth, 210mm (8.268in) diameter sprocket attached to the motor will be

replaced with a 17-tooth 69.1mm (2.72in) diameter sprocket. A chain will connect this 17-tooth

sprocket to a cassette on the main drive shaft which will be just below the motor. The motor

sprocket will be positioned directly in line with the 17-tooth sprocket in the cassette. The user can

shift up and down using a derailleur that is mounted near the cassette. The sprockets on the cassette

were chosen to ensure adaptability of the trike so that it could travel quickly and climb moderate

inclines. The 5-speed cassette allows for a gear ratio range of 0.53 to 1.55. A 5-speed cassette was

used because it was the least number of sprockets required to use a standard size of chain. The chain

selection process to choose 5-speed chain is described in detail in the “Chain” design section. A

sprocket for reverse transmission was not included in the trike. This would add weight and

complexity to the vehicle.

Table 12. List of Sprocket Ratios in Cassette. Speed and Torque measured at 22 Amps to show the

differences in output at each gear ratio.

Teeth Ratio Contribution to Design Speed (mph) Torque (N-m)

11T 1.55 Highest Torque 7.5 66.49

14T 1.21 Intermediate Sprocket 9.7 51.91

17T 1 Intermediate Sprocket 11.7 42.90

20T 0.85 Intermediate Sprocket 13.7 36.46

32T 0.53 Fasted Speed 23.4 21.45

The cassette is affixed to the shaft which turns two other fixed sprockets. One of them is a

16-tooth sprocket that is connected to a fixed sprocket on the rear axle which turns the singular rear

wheel. The other fixed sprocket is a 32-tooth sprocket which is connected via chain to the front

differential. This difference in sprocket sizes allows for a torque split of 67/33 from front to back.

With the 70/30 weight distribution, a 70/30 torque split is ideal for flat ground, as each wheel will

slip at the same time. Any imbalance in the weight left to right would create a greater chance of

tipping on a transverse incline. The 70/30 weight distribution was chosen because it places nearly

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equal weight on each wheel, which a 67/33 distribution would accomplish. Without an equal weight

distribution, the wheel with the least amount of supported weight will slip before the others, placing

an undesirable upper limit on performance. On an incline, the weight shifts to the rear, so more

torque needs to be sent to the rear wheel, and with the designed weight distribution on a 25% grade,

the ideal torque split is 58.7/41.3. The 67/33 split puts HERMES in between the two cases above, a

choice that had to be made based on what normal riding conditions are expected to be. A detailed

calculation can be seen in Appendix F.

The front differential turns two different shafts that drive each of the front wheels

independently. All the chains will be corrosion resistant and should be lubricated approximately

every 300km (186.411miles) and replaced every few years. Tensioners will be placed in the chains

that connect the main drive shaft to the differential and to the rear axle. The steel differential will be

encased in a hard plastic to protect the gears from the elements which will improve the longevity of

the design. The entire drivetrain system can be seen in Figure 8 below. Power is transferred from the

motor to the first stage drive shaft. From the drive shaft, the power is split to the back wheel and the

front differential, which drives the front wheels.

Figure 8. Isometric view of the drive train with chains

For steering, a classic pinion and steering rack ratio was used with a pinion of 30mm

(1.181in) to push the wheels. The rack was connected to control arms mounted on the hub 60mm

(2.362in) away from the center of the wheel. This geometry and a maximum steering wheel angle of

90° allows a maximum wheel angle of 60°, which creates a turning radius of 1.7m (5.577ft) which is

within the desired minimum of 2m (6.562ft). The shaft from the pinion then went to a U-joint to

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add adjustability to the steering wheel. The steering wheel shaft is mounted through bearings and

attached to the plate pin design which is then attached to the frame to give the user the ability to

adjust the height of the steering wheel. The steering wheel is designed with less than 90° of rotation

so that hand-over-hand steering is not necessary. Like a bike, the left side of the steering wheel

controls the front brakes and the right side controls the back brakes. All braking and shifting

systems are available off-the-shelf. A drop-bar integrated brake and road bike style shifter are

integrated onto the steering system. The throttle was designed to be an ATV style push lever for the

right thumb. For a better idea of the form this design would take, see Figure 9 below.

Figure 9. Steering wheel and user controls

The current design of the frame is a tadpole-style with the drivetrain mounted below the

rider. The structure of the frame is constructed out of welded 6162 Aluminum tube stock and has

trussed supports to ensure that it will be able to support the load of the components and the rider.

Ultimately the track, 1.3m (4.265ft), and length, 1.45m (4.757ft), are the minimum dimensions such

that the trike will not tip on a 45 degree transverse incline and will also be narrow and short enough

to maneuver through the trails that it is designed for. The center of mass is located 0.63m (2.067ft)

high, 1.01m (3.314ft) from the rear shaft, and along the center of the frame.

An additional safety feature is a front bumper to protect the rider’s legs in case of a collision.

The rider is safely secured even when completely inverted with a five-point harness which is highly

adjustable and can be easily removed in the case of a crash or tip-over with its center release button.

To put enough weight over the front wheels, the rider will sit front of center, roughly 0.4m (1.312ft)

from the front wheels. The center of gravity results in a front/rear weight distribution of 70/30 and

left/right distribution of 50/50. The seat is designed to reach up to the shoulders of 95% of

persons. Initially seatback angle would range from 40 to 70 degrees; however, the lower end of that

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range was deemed too reclined to be practical. The new lowest angle is 55 degrees. The motor and

battery are to be located towards the front to keep the trike from tipping. The result of all of these

considerations is the full assembly of HERMES shown in Figure 10 below.

Figure 10. Isometric view of HERMES without the rider.

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Powertrain Subsystems

Dimensions:

Overall dimensions Tire diameter: 700mm (27.559in) Length of trike: 2.15m (7.054ft) Wheelbase: 1.30m (4.265ft) Seat angle: 65° Frame length (from axle to axle): 1.45m (4.757ft) Steering – handle to handle: 300mm (11.811in) Steering handle – angle range: ±60°

Differential dimensions Sprocket (“driving gear”) pitch diameter/Teeth: 130mm (5.118in)/32 Outer traverse module: 4.5mm/tooth (0.177in/tooth) Face width: 16mm (0.63in) Spider gear pitch diameter/Teeth: 54mm (2.126in), 12 Side gear pitch diameter/Teeth: 90mm (3.543in), 20 Casing dimension: 110mm (4.331in)

Battery dimensions: 275x210x155mm (10.827x8.268x6.102in)

Sprocket dimensions Cassette

Sprocket 1 (Smallest): 11-tooth, 45.1mm (1.776in) pitch diameter Sprocket 2: 14-tooth, 57.1mm (2.248in) pitch diameter Sprocket 3: 17-tooth, 69.1mm (2.72in) pitch diameter Sprocket 4: 20-tooth, 81.2mm (3.197in) pitch diameter Sprocket 5 (Largest): 32-tooth, 129.6mm (5.102in) pitch diameter

Fixed Drive Sprockets To the Front Differential: 32-tooth, 129.6mm (5.102in) pitch diameter To the Rear Wheel: 16-tooth, 45.1mm (1.776in) pitch diameter Back Sprocket: 16-tooth, 45.1mm (1.776in) pitch diameter Motor Sprocket: 17-tooth, 69.1mm (2.72in) pitch diameter

Chain dimensions: From motor to cassette:

Pitch: 12.7mm (0.5in) Center Distance: 280.94mm (11.061in) Number of links: 70 links

From fixed drive sprocket to front differential: Pitch: 12.7mm (0.5in) Center Distance: 711.2mm (28in) Number of links: 144 links

From fixed drive sprocket to rear wheel: Pitch: 12.7mm (0.5in) Center Distance: 660.4mm (26in)

Number of links: 120 links

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Material used

Trike frame: 6061 Aluminum Alloy

Wheel frame: 6061 Aluminum Alloy

Sprockets: Stainless steel

Differential gears: Grade 1 carburized steel

Steering handle: 6061 Aluminum Alloy with a rubber cover

Chain: Nickel plated steel

Seat: Carbon steel frame with cushion and vinyl cover

Shaft: 4130 Steel Alloy Performance Specs

Motor Capacity: 30 Ah Max Discharge Rate: 60 A

Table 13. Table of Basic Performance-related Specs

Parameter Units Best Case Conditions:

TTS 0-16.09kmh (10mph)

seconds 2.78 4th gear, scaling down current draw perfectly, on asphalt (low rolling resistance)

Top Speed kmh/mph 64.7/40.2 1st gear, long acceleration, on asphalt (low rolling resistance)

Range @ 16.09kmh (10mph)

km/miles 217.9/135.4 1st gear, on asphalt (low rolling resistance)

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System Analysis

Powertrain Efficiency: Table 14. Efficiency Estimates per element.

Part Efficiency

Motor ≥ 85%

Chain (From motor to cassette) ≥ 96%

Chain (From fixed drive sprockets to shafts) ≥ 98% each

Bearings ≥ 99.9% each

Gears ≥ 96%

Differential (only while turning or slipping) ≥ 85%

The total estimated efficiency of the drivetrain is 90%. With the motor included, the

estimated efficiency of the entire drive system from battery to output at the ground is 76%. It is

important to note that while the differential is listed, the inefficiencies are only felt during turning or

slipping when the differential gears are engaged. When turning, the total drivetrain and drive system

efficiency drop to 76% and 65% efficiency respectively.

The chain efficiency was estimated using data summarized by the Cycling Power Lab. The

lab found that, when over 300W is being transmitted, well-maintained chain can operate at 97-98%

efficiency [10]. The chain from motor to cassette was estimated to be less efficient due to cross-

chaining [10]. When the sprockets are not directly inline, additional friction occurs. The bearings

were estimated to be ≥99.9% efficient while supporting the weight of the trike, using equations from

Shigley’s Mechanical Engineering Design [11]. All bearings were included in the overall efficiency. The

differential efficiency was estimated using values provided by the National Programme on

Technology Enhanced Learning [12]. The overall differential efficiency was estimated by multiplying

the efficiency of all four gear meshes.

Chains:

The 3 chains were analyzed using the fatigue analysis for high speed chains outlined in

Shigley’s Mechanical Engineering Design [11]. The life of the 3 chains used are as follows: 2551.94km

(1585.7miles) for motor to driven shaft, 15259.3km (9491.3 miles) for driven to rear shaft, and

42051.68km (26129.7miles) for driven to front shaft. Because of the conservative assumptions made

for design factor, application factor, sprocket ratio, and power output, each of the chains will likely

last longer if properly maintained by the rider.

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The chain selection was based on fatigue life for a chain moving at high speeds which is a

chain velocity of over 50m/min. One special requirement for the chain is that it would need to be

compatible with a multi-speed transmission. This requirement was satisfied by using bike chain to

transfer power from the motor to the driven shaft, which is where the cassette is mounted. It was

necessary to check if a bike chain could theoretically support the loads the motor would put on it.

To ensure that a bike chain would work, a comparable ANSI chain, ANSI 41, was analyzed. The

connections from the driven shaft to the front and back axles were too long for bike chain. ANSI 41

chain was used to transfer power from the driven shaft to the front and rear shafts because it is

more reliable and will not need to shift. The chain that goes from the motor to the driven shaft is a

5-speed KMC chain.

At full throttle the motor can send 800W to the powertrain. To ensure that the estimates for

chain life were conservative it was assumed that the rider would be using all 800W at all times.

Included in the analysis is a design factor of 1.2, and an application factor for impacts of 1.3, which

correlates to machinery with moderate impact. Using the method outlined in Shigley’s Mechanical

Engineering Design [11], chains and their lengths were chosen from the motor to the driving shaft and

then from the driving shaft to the front and rear drive shafts. The chain from the motor to the

driven shaft has the shortest life. Running at 800W with the sprocket ratio set at 32:16 would create

the highest chain velocity with the slowest vehicle motion. The resulting life is 261.7 hours, which at

9.753kmh (6.06mph) is equivalent to 2552.1km (1585.8 miles).

Empirical data on bike chains shows that most bike chains will last around 3218.7-4828km

(2000-3000miles) depending on the care given to them [13]. If the user cleans and lubricates the

chain on a regular basis, which would be every 150km (93.21miles) or so, the bike chain would last

much longer than 2552.1km. Complete calculations for the chain can be seen in Appendix C.

The chain selection also decided exactly how far apart the shafts needed to be from each

other because the length of the chain must match up with an even whole number of links. From the

front shaft to the driven is 711.2mm (28in), driven to motor 280.9mm (11.059in), and driven to rear

660.6mm (26in). Another small alteration was to change the sprocket out of the motor to 17 teeth

instead of 16 teeth which would accommodate the even number of links. An even number of links is

used when possible to avoid needing a specialty link that is more likely to fail.

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Differential:

The differential is located at the front axle of the trike sending power to each of the front

wheels. The load path to the differential starts at the motor, goes through the cassette shaft, and to

the torque splitting sprocket that goes to the front. This 32-tooth torque splitting sprocket sends

approximately 67% of the torque to the receiving 32-tooth sprocket on the case of the differential.

This allows for the torque to be split, but maintains consistent speed to the front and rear axle. Then

the forces were traced through the casing to each spider gear and the transmitted load was found as

a function of torque. The design conditions were based on the bevel gear road map in Shigley’s

Mechanical Engineering Design [11], and iterated geometry until it had a safety factor over 2 for all

design conditions. Two load conditions were considered: heavy shock at the startup torque and very

low speed and medium shock at a trike speed of 16.09kmh (10mph) in the 5th gear, which is the

highest torque gear. The design conditions that did not change were:

90° mesh angle

20° pressure angle

Neither spider or side gears were straddle mounted

Both spider and side gears were made of grade 1 carburized steel

Reliability R = 0.995

Spider gear load cycles 107

Once the design conditions were set Shigley’s fatigue road map and iteration were used to find a final

geometric setup. To get a better idea of the inner configuration of the differential, an exploded view

of the differential has been included in Figure 11.

Table 15. Final dimensions of the differential.

Dimension Value

Outer traverse module 4.5mm/tooth (0.177in/tooth)

Number of side gear teeth 20

Number of spider gear teeth 12

Starting safety factor 2

Case Diameter 110mm (4.33in)

Face width 16mm (0.63in)

Quality Number 6

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Figure 11. Exploded view of the differential.

Cassette Shaft:

The cassette shaft is the second point in the drivetrain. The chain from the motor connects

to a set of 5 sprockets that are used for shifting. A 16-tooth sprocket sends 33% of the torque to the

rear wheel and a 32-tooth sprocket sends 67% of the torque to the front wheels. For the purpose of

this analysis, the chain was assumed to be tensioned on one side only. Torques were analyzed at 70%

of the max torque value, finding the diameter for infinite life. This torque is higher than what the

bike will be run at, but provides an extra layer of protection. 4130 steel quenched and tempered at

205°C was chosen for the shaft given its common use in shaft production. Sprockets are mounted

via a splined keyway to ensure rotational location (the same method used to mount bike cassettes),

and against a seat that is threaded on to ensure side to side location, spaced with Delrin spacers.

Bearings are held in place with retaining rings. The threaded section with a seat was assumed to have

a stress concentration similar to a change in diameter. Stress concentrations from the splined keyway

were assumed to be negligible as the value of the concentration is reduced due to the fact that there

is more than one keyway. Axial loads were neglected, as during normal use there is no axial load

placed on the shaft. There will be axial loads during shifting however, these are very small in

comparison to the bending loads and can be ignored. For the endurance limit, a reliability of 99%

was used. The modified Goodman approach for finding the necessary diameter was used, and was

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iterated because the fatigue stress concentrations depend on diameter. See Appendix D for sample

calculations. The final cassette shaft design can be seen in Figure 12.

Figure 12. Detail Drawing of Cassette Shaft. Bearing Locations are denoted in gray.

(Dimensions in mm)

Front Axle Design:

The front axle shown in figure 13 is the third shaft within the drivetrain, and is 17mm

(0.67in) in diameter. It is driven with 67% of the motor output torque through a 1:1 ratio. The

power is transmitted first through a differential that drives two separate, but symmetrical, shafts on

either side. These shafts are supported by two deep grove ball bearings each. To support the minor

axial loads that result from the differential’s bevel gears, a collar, affixed with a set-screw, is mounted

on each shaft to transmit the axial loads into the first two bearings. These bearings are placed at

50mm (1.97in) from the center of the differential, while the second pair of bearings is mounted

250mm (9.84in) from the center of the differential. Continuing past the second bearing pair, each

shaft is connected to a universal joint to transmit torque through a connecting rod to each free

wheel hub. The shaft was similarly selected to be manufactured from 4130 steel, quenched and

tempered at 205°C as it provides ample strength characteristics, and allows for continuity within

HERMES shaft design. Final shaft dimensions can be found in Table 16.

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Figure 13. Detail Drawing of Front Axle Shaft Right Side. Note: The two shafts are symmetrical for

the left and right side. Bearing locations are denoted in gray. (Dimensions in mm.)

Table 16. Final dimensions of shafts.

Shaft Location Shaft Diameter

Cassette Shaft 20mm (0.787in)

Front Axle Left, Right Primary: 17mm (0.67in), Step-up: 18.53mm (0.73in)

Bearing Selection:

For bearing selection, a life of 6000 hours was selected because it was recommended for

machines used for short or intermittent operation with minimal service interruption. At max speed,

with 700mm (27.56in) diameter wheels, this corresponds to 6.72x107 revolutions, which is used to

compare to the manufacturers rating of 106 ratings. A reliability of 99% was used with the Weibull

distribution. An application factor of 1.25, applicable for light impact, was used to find the C10 value.

While there were no significant axial loads on the cassette shaft support bearings, the differential

produced small axial loads on both the left and right attached shafts. Despite these axial loads, it was

determined that normal 02 series, single-row deep groove ball bearings would suffice for both shafts.

While not designed for significant axial loads, deep grove ball bearings are rated by several

manufacturers including RBC bearings to withstand 0.25-0.5 times the basic static load rating C0, far

greater than any axial loads within the system.

Due to the asymmetric placement of the cassette and sprockets on the rear shaft, the two

bearings experience different radial loads. As such, two different bearings were selected for this

shaft. The bearing on the left side of Figure 12 is larger to accommodate higher loads, while the

bearing of the right is smaller to allow for assembly of the shaft.

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For the front axle shaft, the bearing withstanding the largest load was used to size the

required bearings. For the bearings used next to the free wheel hub to transmit weight and road

bumps into the frame, it was confirmed that the same 17mm (0.67in) bore deep groove ball bearings

was sufficient. This analysis accounted for significantly higher shock because of road bumps and

irregularities. See Appendix E for sample calculations of this analysis.

Table 17. Final sizes for bearings used on each shaft

Location Bearing Type

Cassette shaft left, right support Single-Row 02 Series Deep Grove, 30mm bore, 62mm OD (left side); 20mm bore, 47mm OD (right side)

Front axle support Single-Row 02 Series Deep Grove, 17mm bore, 40mm OD

Cost Analysis:

Cost was estimated using equations and projected prices provided in Professor Fabijanic’s

“ME329 Project Kickoff” [14]. Table 18 shows a detailed break-down of the total cost of the trike.

A base cost of $1900 was used as a starting point. The structure cost was calculated as a function of

the wheelbase and track width. The 6 gears and the gear housing listed are used to make the

differential. The 10 sprockets make up the first two stages of the drivetrain. The derailleur was then

added to the overall cost. Standard parts, including brake pads, fasteners, bearings and control

mechanism, were assumed to be a part of the base cost. The total estimated cost was $5622.49. This

is an acceptable cost for a fully functional electric off-road trike because it is simultaneously less than

Horizon's electric trike, and comparable in price to that of common hand-powered trikes [5]. This

cost makes HERMES accessible to those who cannot afford the Horizon trike but need more

electric support than the hand-crank trikes offer.

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Table 18. Itemized parts list with attached cost.

SYSTEM DESCRIPTION COUNT TOTAL COST

REQUIRED Base 1 $1,900.00

CHASSIS Structure (L*T) 2918 $131.99

ELECTRICAL Motor kit 1 $900.00 Battery 1 $1,053.00

DRIVETRAIN Gear 6 $450.00 Gear Housing 1 $100.00 Sprocket 10 $500.00 Chain 13.75 ft. $137.50 Shaft 6 ft. $300.00 U Joint 2 $100.00

MISC. Derailleur 1 $50.00 Total $5,622.49

Improvements on Initial Design

A roll bar was decided against because of its additional weight and because it would raise the

center of gravity which would compromise the tip-over criteria. To ensure that lateral tip-over

doesn’t occur while traversing an incline, many of the components were moved forward to place

most of the weight between the two front wheels. The original design included a redundant

intermediate shaft which was removed for the final design as it was determined that the differential

could be driven directly by a chain. The wheelbase was also increased slightly to aid with stability.

The possibility of a polymer cover over the lower part of the frame was also a potential

consideration as it would protect the drivetrain from debris and as aesthetic improvements.

However, this would require a thermodynamic analysis of the motor and electronics to ensure that

overheating would not occur in the insulated chamber.

If HERMES makes it to the manufacturing stage, it is still unsure whether the complete

design would be easily manufactured and assembled. It would require further analysis to compare

possible manufacturing techniques. The current design is also a barebones design that lacks potential

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accessories such as water bottle holder or storage for food/first aid kit. In its current state, this

design only details the drivetrain and power systems. Further design of the subsystems and frame

would be required before introduction to market.

Conclusion

HERMES has proved itself to be a high performance and inexpensive trike for the off-road

trike market. It does not require any use of the rider’s legs, allowing for people with lower body

disabilities to access trails they would not otherwise be able to access. It is also equipped with a

powerful 48V DC motor to accommodate riders that aren't strong enough use a conventional hand-

crank trike. It will handle the customer’s requirements of not tipping while traversing, ascending,

and descending moderate inclines, while still maintaining sufficient ground clearance as to not

collide with obstacles on the trail. Adjustable seat positions were included to account for a larger

variety of rider sizes while ensuring comfort. The drivetrain is easily accessible for repairs and

maintenance, and the mode of power transfer has been chosen to extend the life of the parts while

making the trike versatile yet powerful. HERMES could also be manufactured and sold for

significantly less than the one competing product on the market: Horizon All Electric priced at

$13000. HERMES's top speed and hill climbing ability means it can go faster and reach more

extreme trails than its competitor. These design considerations makes HERMES a unique product

that enables an underrepresented demographic to escape the confines of the city and explore the

awe-inspiring outdoors around them, that otherwise would have been completely inaccessible.

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References

[1] U.S. Dept. of Agriculture. (2012, June). Guidelines for Road Maintenance Levels. Retrieved May

30, 2017, from https://www.fs.fed.us/t-d/pubs/pdf/11771811.pdf

[2] Subcommittee D13.55. (2012). Standard Tables of Body Measurements for Mature Men, ages 35

and older, Sizes Thirty-Four to Fifty-Two (34 to 52) Short, Regular, and Tall. ASTM International.

Retrieved May 30, 2017.

[3] Reactive Adaptations. (2017). Bomber Offroad Handcycle. Retrieved May 30, 2017, from

http://www.reactiveadaptations.com/bomber-rs-offroad-handcycle/

[4] Invacare® Top End® Force™ CC Handcycle (n.d.). Retrieved May 30, 2017, from

http://offers.invacare.com/top-end-force-cc-product-overview

[5] Outrider USA. (n.d.). Horizon All Electric (A). Retrieved May 30, 2017, from

https://outriderusa.com/products/horizon-atv-all-electric-a

[6] Science Direct. (January 2011). Analysis of the cracking causes in an aluminium alloy bike frame.

Retrieved June 3, 2017 from

http://www.sciencedirect.com/science/article/pii/S1350630710001317

[7] PingBattery. (2017). What's LiFePO4? Retrieved May 30, 2017, from

http://www.pingbattery.com/whats-lifepo4/

[8] Suzhou Bafang Electric Motor. (2015). Bafang BBSHD MANUAL. Retrieved May 30, 2017,

from https://fasterbikes.eu/de/index.php?controller=attachment&id_attachment=34.

[9] EngineerDog. (2015, September 9). Engineering a 3 Wheel Vehicle Chassis. Retrieved May 30,

2017, from https://engineerdog.com/2015/09/09/engineering-a-3-wheel-vehicle-chassis/

[10] Cycling Power Lab. (2017). Drivetrain Efficiency & Marginal Gains. Retrieved May 30, 2017,

from http://www.cyclingpowerlab.com/DrivetrainEfficiency.aspx

[11] Budynas, R. G., Nisbett, J. K., & Shigley, J. E. (2015). Shigley's Mechanical Engineering Design (10th

ed.). New York, NY: McGraw-Hill Education.

[12] NPTEL. (n.d.). Module 6: Application Of Tribology. Retrieved May 30, 2017, from

http://nptel.ac.in/courses/112102015/29

[13] John Stone Fitness. (October 2014). In depth: When to replace your bike’s chain. Retrieved

June 5, 2017, from http://www.johnstonefitness.com/2014/10/24/in-depth-when-to-replace-your-

bikes-chain/

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[14] Fabijanic, J. (2017). Project Kickoff ME329. Retrieved May 30, 2017, from Polylearn

[15] Fabijanic, J. (2017). Project Primer ME329. Retrieved May 30, 2017, from Polylearn.

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Appendices:

Appendix A. Detail drawing of full CAD model of trike.

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Appendix B. System Trade Study Tools and Results

The majority of the system trade study was done using Excel tables. The important variable

inputs can be changed from a singular page, fed to all other subsequent pages, and outputs are then

displayed. This allows for rapid iteration with different configurations. Important characteristics of

the trike, including weights, performance metrics, dimensions, drivetrain and battery values, and tip-

over criteria are then outputted to the user.

Center of mass (CM) was calculated by finding the CM of individual components in

SolidWorks. Then using the equation

𝐶𝑀𝑥 =∑ 𝑚𝑥𝑖

∑ 𝑚𝑖

(for the x coordinate – similar equation for y and z coordinates), the exact location of the CM was

located for the entire trike. This was checked against the CM that SolidWorks calculated for the

whole trike. The balance of weight between front/rear and left/right was calculated based on the

CM location.

The tip-over trade study tool is based on the equations for lateral and longitudinal forces

found in the project primer [15] and from the calculated center of mass. Easy to see YES/NO boxes

update when dimensions, weights, and positioning change to easily check tip-over criteria.

Acceptable dimensions for track and wheelbase are graphed in Figure 6. An acceptable value was

chosen from here. Lateral tip-over was determined by looking at force on the uphill tire during

traverse of a 45-degree incline, using the equation

𝐹 =

(%𝐹)𝑊𝑡

2−

𝑚𝑔𝑠𝑖𝑛(45°)ℎ

𝑡

Where %F is the percent of weight over the front wheels, Wt is the total weight of the trike and

rider, h is the CG height, t is the track, and gsin(45) represents the equivalent acceleration due to

gravity.

Similarly, for longitudinal tip-over, the force on the front wheel (climbing) and rear wheel

(descending) are as follows

𝐹𝑓 = (%𝐹)𝑊𝑇 −𝑚𝑔𝑠𝑖𝑛(30°)ℎ

𝑡

𝐹𝑟 = (%𝑅)𝑊𝑇 −𝑚𝑔𝑠𝑖𝑛(45°)ℎ

𝑡

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The performance trade study tool calculates the road load, tractive force, torque and

rotational speed at the axle, maximum speed of the vehicle, time to speed, and range. The equations

used are driven by the gear ratio, amperage, and associated values from the Bafang motor curves.

Rolling resistance and amperage are easily adjustable for simple iteration. Fixed values were

protected from being edited. Figure 12 was created to show changes in velocity and power based

upon gear ratio. Figure 12 shows net force available for acceleration at different speeds with a gear

ratio of 0.53. The tractive force line represents positive forces attempting to move the trike forward,

while the road force shows the resistive forces. The net force is the area between the two lines.

Figure 12. Representative graph of road load and tractive force at varying velocities while running

the motor at 22A with a gear ratio of 0.53.

Figure 13 was used in calculating time to speed. Figure 13 shows at every amperage and gear

ratio the net power available to accelerate the trike. The optimal acceleration of the trike would

follow the top of each gear ratio curve, with the trike shifting gears right before each intersection of

the curves. Net power was calculated using the following equation for force and multiplying it by

velocity

𝐹𝑛𝑒𝑡 = 𝐹𝑤ℎ𝑒𝑒𝑙 − 𝐹𝑑𝑟𝑎𝑔 − 𝐹𝑟𝑜𝑙𝑙𝑖𝑛𝑔 𝑟𝑒𝑠𝑖𝑠𝑡𝑎𝑛𝑐𝑒

𝑚𝑎 = (𝑇𝑚𝑜𝑡𝑜𝑟 ∗ 𝜁 ∗ 𝜂𝑡𝑜𝑡𝑎𝑙 ∗ 𝑟𝑤ℎ𝑒𝑒𝑙) − (𝑐𝑟𝑟 ∗ 𝑁) −1

2(𝐶𝐷 ∗ 𝐴𝑠) ∗ 𝜌 ∗ 𝑣2

0

50

100

150

200

250

Forc

e (N

)

Velocity (m/s)

Road Force

Tractive Force

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Tmotor: torque out of motor

ζ: Gear ratio from motor to axle

η: System efficiency

r: Radius of wheel

c: Rolling resistance

N: Normal force

CD: Coefficient of drag

As: Surface area

ρ: Air density

Lookup tables were used for the motor performance, battery pack, rolling resistance and

wheel sizes. These tables allowed for rapid iteration. Changing the value in one place would affect

the change across the entire workbook.

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Figure 13. Plot of net power as a function of gear ratio, velocity, and current. Each data point is

labeled with the operating current.

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Analysis was also done on how to split torque between the front and rear wheels. For a

tadpole design, splitting the torque 50/50 front/rear will result in the rear wheel receiving 50% of

the torque and the two front wheels receiving 25% of the torque each. An issue then arises as the

rear wheel will tend to slip first as it receives more of the torque. Weight distribution also plays a

role. Wheel slipping occurs when the torque applied to the wheel exceeds the static friction moment.

On flat ground, where the front/rear weight distribution is known slipping occurs when 𝑇𝑚𝑎𝑥 =

𝜇𝑠𝑃𝑚𝑔𝑟𝑤ℎ𝑒𝑒𝑙. Where P is the percent of the weight on the front or rear wheel. For HERMES, this

means the front wheels should receive 70% or the total torque, and the rear should receive 30%.

Even though the front two wheels have slightly more torque applied to them, since they have more

weight placed over them, they will resist slipping more than the rear wheel. However, while

climbing, the weight distribution changes. As seen in Appendix F in the sample calculation for

torque splitting, summing the moments can give the normal force that each wheel experiences.

From this, the torque that each wheel can handle so they all slip at the same time was found to be

58.7% to the front axle and 41.3% to the rear axle. A similar analysis could be done with the trike on

a descent, however this was neglected as the rider will not need to use the full capabilities of the

motor while descending. The results are summarized in Table 19 below. It should be noted that at

the current weight of the trike and torque output of the motor, the wheels should not slip under

normal conditions.

Table 19. Torque splitting analysis results.

Surface Max T to front Max T to rear Total Motor T Front % Rear %

[-] [Nm] [Nm] [Nm] [%] [%]

Flat 204.6 89.6 294.2 69.55% 30.45%

Incline 167.6 117.8 285.4 58.72% 41.28%

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Appendix C. Sample Calculation for Chain

First, the initial CAD model was used to find the center distance between the 2 shafts. This number

ended up being 278.26mm (10.955in). To get the right size of chain, the largest sprocket on the

cassette was used as N2. Then the number of links was calculated using the following equation in

which C is center distance, N1 and N2 are number of teeth of the sprockets, and p is pitch which for

a KMC 5-speed bicycle chain is 12.7mm.

For chains, it's advantageous to round up on number of links. This brings the number of links to 69

links and then because a derailleur is being used to shift, another link was added to allow for the

slack required to be able to shift. Once this number was set, the center distance had to be

recalculated.

To find the life of the chain, the following equation was used, where H2 is the horse power out, h is

number of hours, and Lp is the number of links:

The horsepower was calculated using the power out of the motor which is 800W, and a service

factor of 1.3 was used for moderate impact, and a factor of safety of 1.2 was used to ensure that the

calculated life would be for the worst-case scenario.

Tabulated values for KMC 5-speed chain was not found and so the closest equivalent, an ANSI 41

roller chain, was used for this analysis to get an estimate for life. The tabulated power value for

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ANSI 41 chain running at 100 rpm is 0.38 horsepower. The table is based upon the assumptions

that it is rated for 15000 hours, on a 17-tooth sprocket, with a 100 links. The constant was calculated

as follows:

This value was equated to the values for the KMC 5-speed chain that will be used to find the

number of hours.

At 6.06 mph, the slowest speed, the chain will last 1585.76 miles.

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Appendix D. Sample Calculation for Shafts

Diagram:

First the external forces from the sprockets were found. This is assuming there is no axial forces:

Free Body Diagram (x-z plane):

Set the summation of the moments about point A equal to zero to find the reaction at B in the z-

direction:

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Set the summation of the forces in the z-direction equal to zero to find the reaction at A in the z-

direction:

To find the stress concentrations, a sharp fillet was used, and to find the notch sensitivity the notch

radius was assumed to be 2mm. The stress concentration for seating was assumed to be greater than

the keyway stress concentration:

Next was to find the endurance limit, and in order to find the modified endurance limit, it was

assumed that the diameter of the shaft was between 2.79mm and 51mm and that the shaft was

operating at normal temperatures which means kd.is equal to one. It was also assumed that the 4130

Q&T (205°C) steel shaft would be machined or cold-drawn and would have a reliability of 99%.

Since the shaft is under a combination loading, kc is equal to one:

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Cyclic stress was found next. In order to get a conservative estimate, maximum moments and

torques were used. The normal stress due to bending is shown below:

These are combined using the Mod-Goodman criteria:

Because Kf and Kfs both depend on diameter, so iteration was necessary to find the required

diameter of the shaft.

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Appendix E. Sample Calculation for Bearings

To size the bearings, the ratio of rating life to design life was calculated:

Next the C10 was calculated assuming a reliability of 99% in order to find the right bearing size. This

calculation assumes an application factor of 1.25 and use of a ball bearing, so a is equal to 3. This

equation also uses manufacturer data from Shigley's Mechanical Engineering Design that includes x0,

theta, and the constant b. The design force of 1800N was found when designing the shaft:

This loading requires a 02 series, single row, deep groove ball bearing with 30mm inner diameter and

62mm outer diameter with a load rating of 19kN.

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Appendix F. Sample Calculation for Torque Splitting

First the torque split is analyzed on flat ground. Below is a free body diagram of the trike on flat

ground not moving. The center of gravity is assumed to be centered in the x-direction:

Where:

Pf is percent weight over front wheels Pr is percent weight over rear wheels m is total mass of the rider Nf/r is the normal force on the front and rear wheel L is the length of the trike Ff is the friction force r is the wheel radius Tf/r is the torque from the motor front/rear

First the summation of the moments was taken about the contact point of the rear wheel and set to

zero to find the normal force of the front:

Then the summation of the forces in the y-direction were equated to zero:

Free body diagrams of the wheels just before slipping:

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The moments were summed at each of their centers in order to find an expression for the torque on

each wheel:

Comparing the values for Tf and Tr, to the motor output torque give the desired torque splitting.

Now the climbing case is examined. The free body diagram is shown below:

The summation of the moments was taken around the rear contact point in order to find an

expression for the normal force in the front:

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Forces were summed in the y-direction and set equal to zero:

Free body diagrams of the wheels just before slipping:

Moments were summed about the wheel center to find an expression for the torque:

Again, comparing the values for Tf and Tr, to the motor output torque give the desired torque

splitting.

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Appendix G. Sample Calculation for Bevel Gears

Analysis based off of Road map in Shigley’s Mechanical Engineering Design pg. 793.

All figure references and equations from corresponding chapter in Shigley’s

Chosen quantities:

Number of spider gear teeth (Np): 12

Number of side gear teeth (Ng): 20

Outer Transverse Module (met)): 4.5 mm/tooth

Number of spider gear load cycles (nL)P: 107

Reliability (R): 0.995

Case Diameter (dc): 110mm

Transmission Accuracy number (Qv): 6

90° mesh angle

20° pressure angle

Material: Carburized steel

Load Conditions: o Startup (stall torque)= 163.125 Nm /3.78 rpm o Standard operation (10mph)= 50.77 Nm /123.3 rpm

Transmitted load/Speed/Geometry:

Spider Gear Diameter:

𝑊𝑡 =1000𝑇

2𝑑𝑐

= 230.76 for Standard Operation = 741.48 for Startup

Spider Gear Diameter:

𝑑1 = 𝑁𝑝𝑚𝑒𝑡

= 54mm

Side Gear Diameter:

𝑑2 = 𝑁𝑔𝑚𝑒𝑡

= 90mm

Spider Gear Speed:

𝑛1 =𝑑2

𝑑1𝑛2

= 205.28 for Standard Operation = 6.29 for Startup

Side Gear Speed:

n2 is from trade study tts sheet

= 123.28 for Standard Operation = 3.78 for Startup

Spider pitch angle:

𝛾 =𝑁𝑝

𝑁𝑔

= 0.54 rad or 31°

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Cone distance:

𝐴0 =𝑑1

2sin (𝛾)

= 52.47mm

Face width:

𝑏 = 0.3𝐴0

= 16mm

Driven Factors:

Overload Factors: KA found in Table 15-2 pg. 783

= 1.5 for Standard operation condition = 1.75 for Startup condition

Dynamic Factor:

𝐾𝑣 = (𝐴 + √200𝑣𝑒𝑡

𝐴)

𝐵

Where:

𝐴 = 50 + 56(1 − 𝐵) = 59.77

𝐵 = 0.25(12 − 𝑄𝑣)2/3 = 0.8255

𝑣𝑒𝑡 = 5.236(10−5)𝑑𝑝𝑛𝑝 = 0.581 𝑚/𝑠

= 1.146 Size Factor for Bending:

= 0.5242

Size Factor for Pitting Resistance :

= 0.5162

Load-Distribution Factor:

𝐾𝐻𝛽 = 𝐾𝑚𝑏 + 5.6(10−6)𝑏2

Kmb = 1.25 = 1.251

Crowning Factor for Bending Strength:

= 1.5

Pitting Resistance Geometry Factor:

ZI found in figure 15-6 pg. 786

= 0.055

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Bending Strength Geometry Factor:

YJ found in figure 15-7 pg. 786

= 0.164 for side gear = 0.195 for spider gear

Stress-Cycle Factor for Pitting Resistance:

= 1.361 for side gear = 1.32 for spider gear

Stress-Cycle Factor for Bending Strength:

= 1.017 for side gear = 0.999 for spider gear

Hardness Ratio Factor: ZW: All gears made from same material, so assume

Brinell hardness the same.

= 1

Temperature Factor:

= 1

Reliability Factors:

𝑍𝑍 = √𝑌𝑍

= 1.075 = 1.037

Allowable Contact Stress Number: For carbureted steel sH lim:

Grade 1 1380 MPa Grade 2 1550 MPa Grade 3 1720 MPa

= 1380 MPa

Allowable Contact Stress Number: For carbureted steel sF lim:

Grade 1 205 MPa Grade 2 240 MPa Grade 3 275 MPa

= 205 MPa

Elastic Coefficient for Pitting Resistance:

ZE for steel is roughly 190 √𝑀𝑃𝑎

= 190 √𝑀𝑃𝑎

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Bending:

Side Gear Bending Stress:

(𝜎𝐹)𝑆𝑖𝑑𝑒 =𝑊𝑡

𝑏

𝐾𝐴𝐾𝑣

𝑚𝑒𝑡

𝑌𝑥𝐾𝐻𝛽

𝑌𝛽𝑌𝐽

Startup: (sF)Side= 73.97 MPa Standard Operation: (sF)Side = 22.05 MPa

Spider Gear Bending Stress:

(𝜎𝐹)𝑆𝑝𝑖𝑑𝑒𝑟 = (𝜎𝐹)𝑆𝑖𝑑𝑒

(𝑌𝐽)𝑆𝑝𝑖𝑑𝑒𝑟

(𝑌𝐽)𝑆𝑖𝑑𝑒

Startup: (sF)Spider = 62.21 MPa Standard Operation: (sF)Spider = 18.54 MPa

Side Gear Bending Strength:

𝜎𝐹𝑃 = 𝜎𝐹 𝑙𝑖𝑚𝑌𝑁𝑇

𝑆𝐹𝐾𝜃𝑌𝑍

(sFP)Side = 96.9 MPa

Spider Gear Bending Strength:

𝜎𝐹𝑃 = 𝜎𝐹 𝑙𝑖𝑚𝑌𝑁𝑇

𝑆𝐹𝐾𝜃𝑌𝑍

(sFP)Spider = 95.32 MPa

Side Gear Safety Factors:

𝑆𝐹 =𝜎𝐹𝑃

𝜎𝐹𝑆𝐹

Startup: SF = 2.62 Standard Operation: SF = 8.79

Spider Gear Safety Factors:

𝑆𝐹 =𝜎𝐹𝑃

𝜎𝐹𝑆𝐹

Startup: SF = 3.06 Standard Operation: SF = 10.28

Wear:

Contact Stress:

𝜎𝐻 = 𝑍𝐸 (𝑊𝑡

𝑏𝑑𝑍𝐼𝐾𝐴𝐾𝑣𝐾𝐻𝛽 𝑍𝑥𝑍𝑥𝑐)

1/2

Startup: sH = 989.97 MPa Standard Operation: sH = 540.54 MPa

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Side Gear Contact Strength:

𝜎𝐻𝑃 = 𝜎𝐻 𝑙𝑖𝑚𝑍𝑁𝑇𝑍𝑊

𝑆𝐹𝐾𝜃𝑌𝑍

(sHP)Side = 1280.61 MPa

Spider Gear Contact Strength:

𝜎𝐻𝑃 = 𝜎𝐻 𝑙𝑖𝑚𝑍𝑁𝑇𝑍𝑊

𝑆𝐹𝐾𝜃𝑌𝑍

(sHP) = 1241.83 MPa

Side Gear Safety Factors:

𝑆𝐻 =𝜎𝐻𝑃

𝜎𝐻𝑆𝐻

Startup: SH = 2.36 Standard Operation: SH = 7.94

Spider Gear Safety Factors:

𝑆𝐻 =𝜎𝐻𝑃

𝜎𝐻𝑆𝐻

Startup: SH = 2.23 Standard Operation: SH = 7.46