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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.