Geometric Design of Spatial Mechanisms for Interaction with the Environment

This work proposes a theoretical foundation for creating spatial mechanisms for interaction with the environment through a general geometric model. In the proposed model the curvature of the objects in the environment (or the curvature of the environment itself) in the vicinity of a specified location is approximated by virtual spheres with known radii that shape the motion of the moving body/workpiece. It is shown how the conditions on spatial velocities and accelerations of the moving body derived from the geometric model can be directly incorporated in the kinematic design task to shape the motion of spatial mechanisms. The theoretical foundation for creating spatial mechanisms based on the proposed general geometric model is crucial in gaining understanding of mechanism-environment interactions and is a new contribution.