Workspaces of planar parallel manipulators

Abstract

This paper presents geometrical algorithms for the determination of various workspaces of planar parallel manipulators. Workspaces are defined as regions which can be reached by a reference point C located on the mobile platform. Firts, the constant orientation workspace is determined. This workspace is defined as the region which can be reached by point C when the orientation of the moving platform is kept constant. Then, the maximal workspace, which is defined as the region which can be reached by point C with at least one orientation, is determined. The maximal workspace is also referred to as the reachable workspace. From the above regions, the inclusive workspace, i.e. the region which can be attained by point C with at least one orientation in a given range, can be obtained. Then, the total orientation workspace, i.e. the region which can be reached by point C with every orientation of the platform in a given range, is defined and determined. Finally, the dextrous workspace, which is defined as the region which can be reached by point C with any orientation of the platform, can be determined. Three types of planar parallel manipulators are briefly described and one of them is used to illustrate the algorithms. Each of the workspaces is determined here for this type of manipulator while the derivations for the other types of manipulators will be presented in another paper. The algorithms developed here are useful in the design and motion planning of planar parallel manipulators.