Generating the Swept Area of a Body Undergoing Planar Motion

Abstract

The swept area of a two-dimensional object undergoing motion in its plane of definition is the union of the area occupied by the object at all positions during the motion. A methodology for determining a close approximation to an exact swept area of a convex object with a known arbitrary motion is developed here. The resulting swept areas are used as constraints in the geometric design of the links in an interference-free complex planar mechanism. Criteria for determining individual points falling on the border of the swept area are derived from envelope theory. These points are determined at a reference position of the sweeping body using generalized moving centrodes. The swept area is constructed from these points plus sections of the border of the moving body at some selected positions. Overlap of the swept area onto itself, caused by the body moving back to an area which it occupied previously, is processed by dividing the overall swept area into sub swept areas which are free of overlap. An eleven-step swept area generation algorithm is presented along with an example.