2011 IEEE IROS, September 28, 2011

1. 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

2. Base Base 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.

3. Prior Work • “Spherical” can mean any combination of yaw, pitch, roll, and radial (prismatic). Non-spherical, suitable for general rendering Spherical, not suitable for general haptic rendering with translation 2-DOF yaw and pitch 3-DOF yaw, pitch, and roll about hand

4. yaw, pitch, and radial (flown) yaw, pitch, and radial (grounded, cable in flexible sleeve)

5. yaw, pitch, roll, and radial (flown, friction rollers) yaw, pitch, roll, and radial (all grounded, complicated cabling)

6. Overall Device • Spherical coordinates yaw, pitch, and prismatic radial

7. 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.

8. 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.

9. 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.

10. Wheel Profile • Point contact essential for efficiency and predictable gear ratio. • If line contact, energy loss and unknown gear ratio.

11. 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. η E Aluminum: highest metal-metal μ, lowest metal η, cheap, easily-machined, durable, and light-weight

12. 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.

13. Design: Radial DOF

14. Design: Radial DOF

15. Design: Gimbal • 2-DOF sensed only. • Same aluminum-aluminum friction differential, only smaller (1/5th). • Magnet for automatic homing.

16. Device Physical Characteristics

17. 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.

18. *82% higher than max continuous force for Sensable Omni

19. Friction • 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.

20. Dynamic Range • Dynamic range D = Max peak isotropic force/stiction. • Sensable Omni has dynamic range of 12.7 Dynamic Range, Our Device

21. 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.

22. 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.

23. Questions?

24. 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.

25. Differential Transformation • To go from motor angles and torques to pitch, yaw angles and torques:

26. FWD Kinematics, Jacobian

27. Gravity Compensation • Active gravity compensation used to make device float, saving effort on the user’s part.