Practical Force-Motion Models for Sliding Manipulation

Abstract

The goal of this article is to develop practical descriptions of the relationship between forces and motions in sliding manipulation. We begin by reviewing the limit surface, a concept from the mechanics of sliding bodies that uses kinematic analysis to find the force and moment required to produce any given sliding motion. Next we provide experimental results showing that the limit surface only approximates the actual force-motion relationship. Then we look at other approximations that can be used to provide a simplified model useful in control, planning, and simulation of manipulation. These approximations include square pyramids, cones, ellipsoids, and ellipsoids with facets removed. Different approximations may be most appropriate, depending on the required computational speed and accuracy and the need to produce conservative results.

Dynamic Multi-Rigid-Body Systems with Concurrent Distributed Contacts: Theory and Examples

“…Following in the footsteps of Lötstedt and others who have popularized the use of complementarity methods in rigid body dynamics [7,8,11], we extend the model developed formally in [15] to include a frictional moment (transmitted about the contact normal). While it is not possible to transmit such a moment through a point contact (as would occur generically between curved rigid bodies), we include it in our model in recognition of the fact that contacts between stiff real bodies are distributed over small patches [6] and that the friction forces obey the maximum work inequality [5]. While in principle, the geometries of the contact patches could be arbitrary, the supporting empirical data presented in [6] and the leveraged theory in [5] assumed that contact patches were planar.…”

“…While it is not possible to transmit such a moment through a point contact (as would occur generically between curved rigid bodies), we include it in our model in recognition of the fact that contacts between stiff real bodies are distributed over small patches [6] and that the friction forces obey the maximum work inequality [5]. While in principle, the geometries of the contact patches could be arbitrary, the supporting empirical data presented in [6] and the leveraged theory in [5] assumed that contact patches were planar. Thus we include that assumption here.…”

Towards a Realistic and Self-Contained Biomechanical Model of the Hand

“…There may be multiple solutions to a particular problem (ambiguity) or there may be no solutions (inconsistency) (Erdmann, 1994). Finally, the soft contact model is used to model the contact between a soft finger and a rigid object allowing the finger to apply an additional torsional moment with respect to the normal at the contact point (Ciocarlie et al, 2005(Ciocarlie et al, , 2007Howe et al, 1988;Howe & Cutkosky, 1996;Kao & Cutkosky, 1992;Kao & Yang, 2004). A typical contact between a soft finger and a contact surface can be modelled by the Hertzian contact model (Hertz, 1882;Johnson, 1985).…”

Macroscopic diagnostics of microscopic friction phenomena

“…[5,6,7]. It was shown that the sliding friction of a circular disk is reduced if the contact is also spinning with relative angular velocity ω -a phenomenon which plays an important role in various games such as curling or ice hockey [8,9,10].…”

“…Apart from the limit of pure sliding ε → ∞, where F → 1, the functions F (ε) and T (ε) depend on the pressure distribution across the contact area [5,6,11]. Assuming uniform pressure over the area of the disk these functions have been evaluated analytically, describing the coupling of force and torque of a circular disk in the sliding case [7].…”