Haptic Rendering of Compliant Shapes

Dynamically controlling the shape of an object by means of a 3-D shape interface offers many new opportunities in the fields of virtual reality and design as direct exploration of objects becomes feasible. Using a parallel kinematics as 3-D shape interface comes with features such as high stiffness and speed, but requires a series of points to be controlled simultaneously and loop constraints to be met. In this paper we present an approach of controlling the shape of a 3-D parallel kinematics. Shape, loop constraints, and constraints resulting from the user interaction are considered in the form of a hierarchical framework and joint limitations are taken into account. Two alternative control modes for stiff and compliant objects are presented. Implicit surfaces as well as polygon sets represent the input for the virtual shape to be rendered. Results show that the calculation of the inverse kinematics can be achieved with a sampling rate of 1 kHz, independent of the representation of the shape as implicit surface or polygonal set, guaranteeing a sufficiently high sampling rate typical for haptic devices.