1. On the use of Eddy Current Brakes as Tunable, Fast Turn-on, Viscous Dampers for Haptic Rendering
Andrew H. Gosline, Gianni Campion, and Vincent Hayward
Haptics Laboratory, Center for Intelligent Machines
McGill University
Montréal, Québec, Canada
{andrewg, champ,
Haptics Laboratory

2. Motivation Physical damping is required for passivity.
[Colgate and Schenkel, 1994]
Sources of physical damping:
Dry Friction
Viscosity
Electromagnetic
Dissipation is accidental byproduct of design.
Difficult to model and not programmable.
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3. Prior Work
Shunting a DC motor creates electrical damping. [Mehling and Colgate, 2005]
Frequency dependent, not programmable, and limited to back EMF of DC motor.
Magnetorheological (MR) particle brakes are programmable.
Nonlinear, slow to actuate, and suffer from hysteresis [An and Kwon, 2004], [Gogola and Goldfarb, 1999], [Arcy, 1996]
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4. Proposal Eddy current brakes (ECBs) are:
Programmable
Fast turn-on
Linear
Friction free
Inexpensive
Add ECB to each driven joint of the Pantograph.
Identify behavior of ECBs at haptic speeds.
Use physical damping to stabilize renderings.
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5. Eddy Current Brake Physics
Current flows through conductor in loops
J = V x B
F = J x B
Tends to be an ‘end effect’ because path is shorter
B0 in Z direction, plate motion in Y [Heald, 1988]
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6. Eddy Current Brake Physics (cont’d)
Induced current density:
|J| = R|B|
Power dissipated:
Pd = 0.25   D2 d B2 R2 2
Resistive torque:
d= 0.25   D2 d B2 R2 
[Lee and Park, 1999] d D R
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7. Prototype Haptic Device
Concentric aluminum blade added to each base joint of Pantograph.
Toroidal electromagnet cores machined from iron and wrapped with 24g enamel coated magnet wire.
Thin slot in each magnet core to minimize loss.
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8. Damping Characteristics
Energy balance approach from two rest states.
Small and large deflections.
Results indicate linear behavior at typical haptic speeds.
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9. Damping Characteristics (cont’d)
Current to damping ratio trend required.
Theory states a quadratic trend.
Experiments show saturation curve.
Core saturation, blade constraints.
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10. Fast Turn-on Haptic actuators require fast update rate.
Quanser LCAM current driver, 48V supply.
~200Hz update rate possible with ‘off-the-shelf’ components.
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11. Rendering Results - Wall
Manipulandum thrust and held against virtual wall by elastic band .
Dampers on during wall penetration.
Limit cycles quenched or reduced.
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12. Rendering Results - Friction
Friction model by Hayward and Armstrong prone to limit cycles in elastic ‘stuck’ region.
Dampers used only in stuck state.
Limit cycles quenched.
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13. Damping in the Workspace
Joint torques from ECBs translate through Jacobian to manipulandum.
Jacobian not diagonal therefore end effector damping matrix not diagonal.
Possible to compensate for off diagonal terms with motors.
Gives consistent feel throughout workspace.
Not verified experimentally, yet.
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14. Limitations Damper blades add considerable inertia to the device.
Considerable power is required to generate damping torque.
Large ‘C’ shaped magnets flex and release under electromagnetic force, generating vibrations that are both audible and palpable.
Damping is not homogeneous through the workspace.
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15. Conclusions Future Work ECBs are linear dampers at haptic speeds.
Physical damping from ECBs can stabilize renderings of walls and friction.
Future Work
Optimize design for both electromagnetic and dynamic performance.
Explore programmable damping in future control/passivity-observer experiments.
Haptics Laboratory