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, hayward}@cim.mcgill.ca Haptics Laboratory

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. Haptics Laboratory

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] Haptics Laboratory

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. Haptics Laboratory

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] Haptics Laboratory

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 Haptics Laboratory

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. Haptics Laboratory

Damping Characteristics Energy balance approach from two rest states. Small and large deflections. Results indicate linear behavior at typical haptic speeds. Haptics Laboratory

Damping Characteristics (cont’d) Current to damping ratio trend required. Theory states a quadratic trend. Experiments show saturation curve. Core saturation, blade constraints. Haptics Laboratory

Fast Turn-on Haptic actuators require fast update rate. Quanser LCAM current driver, 48V supply. ~200Hz update rate possible with ‘off-the-shelf’ components. Haptics Laboratory

Rendering Results - Wall Manipulandum thrust and held against virtual wall by elastic band . Dampers on during wall penetration. Limit cycles quenched or reduced. Haptics Laboratory

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. Haptics Laboratory

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. Haptics Laboratory

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. Haptics Laboratory

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