[pdf] D. Montana, The Kinematics of Contact and Grasp, International Journal of Robotics Research, 1988
The kinematics of contact describe the motion of a point of contact
over the surfaces of two contacting objects in response to a relative
motion of these objects.
Using concepts from Differential Geometry,
I derive a set of equations, called the contact equations, which
embody this relationship.
I employ the contact equations to design the following applications to
be executed by an end effector with tactile sensing
capability: 1) determining the curvature form of an
unknown object at a point of contact and 2)
following the surface of an unknown object.
The contact equations also serve as a basis for an investigation of the
kinematics of grasp.
I derive the relationship between the relative motion of two fingers
grasping an object and the motion of the points of contact over the
Based on this analysis, we explore the following applications:
1) rolling a sphere
between two arbitrarily shaped fingers, and 2) fine grip adjustment,
i.e. having two fingers which grasp an unknown object locally optimize
their grip for maximum stability.