In this paper, we present a principled method to model gen- eral planar sliding motion with distributed convex contact patch. The effect of contact patch with indeterminate pressure distribution can be equivalently modeled as the contact wrench at one point contact. We call this point equivalent contact point. Our dynamic model embeds ECP within the equations of slider's motion and friction model which approx- imates the distributed contact patch, and eventually brings us a system of quadratic equations. This discrete-time dynamic model allows us to solve for the two components of tangential friction impulses, the friction moment and the slip speed. The state of the slider as well as the ECP can be computed by solving a system of linear equations once the contact impulses are computed. In addition, we derive the closed form solutions for the state of slider for quasi-static motion. Furthermore, in pure trans- lation case, based on the discrete-time model, we present the closed form expressions for the friction impulses the slider suffers and the state of it at each time step. Simulation examples are shown to demonstrate the validity of our approach.
"Manipulation" refers to a variety of physical changes made to the world around us. Mechanics of Robotic Manipulation addresses one form of robotic manipulation, moving objects, and the various processes involved---grasping, carrying, pushing, dropping, throwing, and so on. Unlike most books on the subject, it focuses on manipulation rather than manipulators. This attention to processes rather than devices allows a more fundamental approach, leading to results that apply to a broad range of devices, not just robotic arms. The book draws both on classical mechanics and on classical planning, which introduces the element of imperfect information. The book does not propose a specific solution to the problem of manipulation, but rather outlines a path of inquiry.