Generating the Swept Area of a Body Undergoing Planar Motion

Abstract

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 for a known arbitrary motion is developed here. The methodology has use for preventing interference between links of a planar mechanism during synthesis. Criteria for determining individual points falling on the border of the swept area from the body during any instant of the motion are derived from envelope theory. Points on the swept area boundary are determined at the initial position of the sweeping body for computational efficiency. The swept area is constructed from these points plus sections of the border of the moving body at select positions. Overlap of the swept area onto itself is handled by splitting the overall swept area into a small number of individual swept areas free of overlap. An eleven-step swept area algorithm is clarified with an example.