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![Page 1: 1 A Friction Differential and Cable Transmission Design for a 3-DOF Haptic Device with Spherical Kinematics 2011 IEEE IROS, September 28, 2011 Reuben Brewer.](https://reader035.fdocuments.net/reader035/viewer/2022062321/56649e0d5503460f94af6963/html5/thumbnails/1.jpg)
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A Friction Differential and Cable Transmission Design for a 3-DOF Haptic
Device with Spherical Kinematics
2011 IEEE IROS, September 28, 2011
Reuben Brewer1, Adam Leeper1, and J. Kenneth Salisbury1,2,3
Departments of Mech. Engineering1, Computer Science2, and Surgery3
Stanford University, USA
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Motivation
Need a haptic device that is Compact, with single-link connection
to the user’s hand. More elegant. Easier to stow in a base, haptic
workstation, or table-top. Scalable. Useful for general, as well as specific
(laparoscopic) rendering.
Solution: Spherical Coordinates Concentrate motors in base for slim
form-factor with single link to hand.
Base
Base
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Prior Work “Spherical” can mean any combination of yaw, pitch, roll, and radial (prismatic).
Non-spherical, suitable for general rendering
Spherical, not suitable for generalhaptic rendering with translation
2-DOF yaw and pitch
3-DOF yaw, pitch, and roll about hand
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yaw, pitch, and radial (flown) yaw, pitch, and radial
(grounded, cable in
flexible sleeve)
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yaw, pitch, roll, and radial
(flown, friction rollers)
yaw, pitch, roll, and radial
(all grounded, complicated cabling)
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Overall Device Spherical coordinates yaw, pitch, and prismatic radial
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Device Kinematics Spherical coordinates
Pitch Φ on range [-50°, 30°]. Yaw γ on range [-25°, 25°]. Radial ρ (prismatic) on range [195.5mm, 282mm], for a length of
86.5mm.
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Our Device, Overview Main design contributions:
All grounded, simple, and robust 3-DOF (active) spherical design.
Aluminum-aluminum friction differential. Novel cabling of radial DOF. 2-DOF sensed gimbal with same friction
differential.
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Design: Aluminum Friction Differential Benefits
Parallel structure. Motors easily grounded. Differential is hollow. Zero backlash. Fewer parts. Safe slipping, not breaking.
Main design issues Wheel profile. Material.
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Wheel Profile Point contact essential for
efficiency and predictable gear ratio. If line contact, energy loss
and unknown gear ratio.
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Friction Differential: Material Basic material properties: Cheap, strong, easily-machined, durable, and light-weight. No exotic materials,
plastics, or ceramics. Friction Coefficient μ.
Higher μ = higher force transfer.
Loss Coefficient η Lower η = less energy lost
to elastic hysteresis.
Aluminum: highest metal-metal μ, lowest metal η, cheap,
easily-machined, durable, and light-weight
η
E
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Design: Radial DOF Novel cable transmission routing from a grounded motor
through the differential to actuate prismatic, radial DOF. Must route along path of zero arc-length change ΔS (through
rotational axes, center). Practically, ΔS = 0.02mm, for a max strain of 2.5x10-5 and max internal
tension increase of 0.98N. Tiny lever arm = negligible effect on any DOF.
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Design: Radial DOF
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Design: Radial DOF
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Design: Gimbal 2-DOF sensed only. Same aluminum-aluminum friction
differential, only smaller (1/5th). Magnet for automatic homing.
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Device Physical Characteristics
Omni Ours
Weight 1.8 kgf (4.0 lbf) 2.5 kgf (5.5 lbf)
Footprint See Picture
Workspace Bounding Box Nearly identical 160mm x 120mm x 68mm
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Maximum Isotropic Force What is the largest force that we are guaranteed to be
able to exert in any direction at any configuration? Motor saturation as limit, never the differential slipping.
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Continuous Peak
FMAX, No Grav Comp 1.60N* 7.45N
FMAX, Grav Comp 0.82N 6.79N
*82% higher than max continuous force for Sensable Omni
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Friction
Torque (Nmm) Fwrist, retracted (N) Fwrist, extended (N)
Pitch 67.1 0.34 0.24
Yaw 115 0.59 0.41
Radial n/a 0.93 0.93
Fpitch < Fyaw < Fradial
Pitch DOF has bearing friction only. Yaw DOF adds in friction of the differential wheels rolling. Radial DOF has friction of 9 redirect pulleys + linear slide.
Anisotropic friction noticeable only in free-space, not in contact with virtual models.
Russo radial DOF had friction of 9N, uncompensated, and 1N, compensated.
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Dynamic Range
No Grav Comp With Grav Comp
Min (Z0, radial stiction only) 7.3 8.0
Max (X0, pitch stiction only) 28.3 31.0
Dynamic range D = Max peak isotropic force/stiction. Sensable Omni has dynamic range of 12.7
Dynamic Range, Our Device
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Effective Mass Fairly isotropic
Maximum of 61% spread between min, max in Λ matrix. Sensable Omni has effective mass that is 38% of our max
effective mass.
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Summary A more slender, compact, simple, and robust design for
a spherical haptic device for general haptic rendering. Comparable forces, workspace, and physical properties
to Sensable Omni.
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Questions?
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Prior Work: Details “Spherical” can mean any combination of yaw, pitch, roll, and radial (prismatic)
Impulse Engine 2000 (Immersion Corporation) 2-DOF pitch and yaw, user’s hand on surface of fixed-radius sphere.
L. Birglen, C. Gosselin, N. Pouliot, B. Monsarrat, and T. Lalibert´e, “Shade, a new 3-dof haptic device,” IEEE Transactions on Robotics an Automation, vol. 18, no. 2, pp. 166–175, 2002. 3-DOF yaw, pitch, and roll torques centered about user’s hand.
M. Smith, “Tactile interface for three-dimensionsal computersimulated environments: Experimentation and the design of a brakemotor device,” MS Thesis, MIT, 1988. 3-DOF yaw, pitch, and prismatic radial. Radial transmission was “flown” so that it moved with yaw and pitch.
M. Russo, “The design and implementation of a three degree of freedom force output joystick,” MS Thesis, MIT, 1990. 3-DOF yaw, pitch, and prismatic radial. Radial DOF uses grounded motor and bike-cable type transmission.
U. Spaelter, T. Moix, D. Ilic, H. Bleuler, and M. Bajka, “A 4-dof haptic device for hysteroscopy simulation,” IEEE/RSJ IROS, pp. 3257–3263, 2004. 4-DOF yaw, pitch, roll, and prismatic radial. Roll and radial DOF motors “flown”, and radial DOF actuated via
friction rollers.
P. Gregorio, N. Olien, D. Bailey, and S. Vassallo, “Interface apparatus with cable-driven force-feedback and four grounded actuators,” U.S. Patent 7 404 716, 2008. 4-DOF yaw, pitch, roll, and prismatic radial. Grounds all 4 motors, but has very complicated cabling system.
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Differential Transformation To go from motor angles and torques to pitch, yaw
angles and torques:
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FWD Kinematics, Jacobian
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Gravity Compensation Active gravity compensation used to make device float,
saving effort on the user’s part.