BiomechanicsTorques and moments of force

Define Torque and identify the factors affecting torque

Differentiate between the different classes of levers.

Demonstrate the ability to calculate torques and muscular torques

Lesson Objectives

A torque is the turning effect that is produced by a force

◦ Can also be known as a moment of force.◦ or simply a moment.

Torque

Torque Lay a book flat on a table.

◦ Where does the books centre of gravity lay.

Apply a force through the books top edge just off the books centre of gravity◦ What happened?

Repeat a number of times, each time, strike the book so the line of action is farther away from the centre of gravity◦ What happened?

What factors affect torque?

◦ Distance between the line of action of action and the axis of rotation

◦ Size of the force

Factors affecting Torque

So we can define Torque as ◦ The turning effect produced by a force and is

equal to the product of the magnitude of the force and the distance between the line of action of the force and the axis of rotation to the object

The distance between the line of action of the force and the axis of rotation (a) is the perpendicular distance between the line of action of the force and a line parallel to it that passes through the axis of rotation.

Factors affecting Torque

This can be simply defined as the moment arm, and can be seen in the diagram as r

Mathematically, torque can be defined as:

◦T = F x r

◦ Where◦ T = torque (Nm)◦ F = Force (N)◦ R = moment arm (m)

Torque

Note Torque is a vector quantity, You must specify a direction

(+) (-)Counter clockwise Clockwise

The width of a door is 80 cm. If it is opened by applying a force of 20 N at its edge (away from the hinges), calculate the torque produced which causes the door to open.

Example

Solution : Length of lever arm = 40 cm = 0.40 m (since distance between axis of rotation and line of action of

force is 40 cm)Force applied = 20 NT = F x r   = 20 x 0.8   = 16 Nm (8 Newton meter)Answer : Torque = 16 Nm

In the previous question, if the handle of the door is situated 20 cm from the edge, and we know the torque required to open the door is 16Nm, What is the force applied through the handle to open the door?

Example 2

Solution : Length of lever arm = 80 cm - 20 cm = 60 cm = 0.60m Torque = F x r      16N = F x 0.60

          F = 16/0.6

Answer : Force = 26.7 N

A lever is a rigid object that is used with an axis to either multiply the mechanical force (effort) or resistance force (load) applied to it.

Levers

There are 3 components to a lever Axis (pivot or fulcrum)

Resistance load (weight)

Force (effort)

The fulcrum is located between the applied force and the load

The load is situated between the fulcrum and the force

The force is applied between the fulcrum and the load

Muscles create the torques that turn our limbs. When a muscles contracts it pulls on its points of attachment, along a line of action (or line of pull)

Muscular Torques

Because the line of action of the muscle force is some distance from the joint axis (fulcrum) a moment arm exits (r)

Consider how the moment arm (r) changes as the arm flexes

Muscular Torques

What affect does that have on the biceps brachii’s ability to create a torque about the elbow joint?

As the forearm is flexed and extended, the moment arm changes.◦ The moment arm is biggest when the elbow is at 90

degrees, and gets smaller as it is flexed and extended away from this position.

Muscular Torques

A similar situation exists for most of our muscles and the joints they cross.

Explains why our muscles are apparently stronger in some joint positions than others

As muscle attachments are much closer to the joint axis than the load, muscles have to create large forces just to hold a static position.

You are holding a 20kg dumbbell in an isometric position with your elbow at 90 degrees. The moment arm of the dumbbell is 30cm about the elbow joint axis.◦ What torque is created by this dumbbell about your joint

axis?

Muscular Torques

T = F x r T = 200 N x 0.3 T = 600 Nm

To hold the dumbbell in this isometric position your elbow flexor muscles, must create a clockwise torque equal to the counter clockwise torque created by the dumbbell.

If the muscle attachment is 5cm from the joint axis, what force must they pull at to keep the dumbbell in this position?

Muscular Torques

T = F x r 600 Nm = F x 0.05m F = 600 / 0.05 F = 1200N

The Achilles tendon inserts on the calcaneus (heel bone) at a distance of 8 cm from the axis of the ankle joint. If the force generated by the muscles attached to the Achilles tendon is 3000N, and the moment arm of the force about the ankle joint is 5cm, what torque is created by these muscles about the ankle joint?

Problem

An athlete is doing a knee extension exercise using a 100 N dumbbell. She holds her leg so that the horizontal distance from her knee joint to the dumbbell is 30cm.◦ (a) For this position what torque is created by the

dumbbell about her knee joint axis?

◦ (b) If the moment arm of the knee extensor muscles is 4cm about the knee joint axis, what amount of force must the muscles produce to hold the leg in the position described.

Problem

An athlete is attempting to lift 15kg. The moment arm of the this weight about his elbow joint s 25cm. The force created by the elbow flexor muscles is 2000 N. The moment arm of the elbow flexor muscles is 2cm.

◦ Is the athlete able to left the weight with this amount of force in his flexor muscles?

Problem

We can define Torque and identify the factors affecting torque

We can differentiate between the different classes of levers.

We Can demonstrate the ability to calculate torques and muscular torques

To Conclude