A simplified approach for obtaining the workspace of a class of 2-dof planar parallel manipulators

This paper presents a method for generating the reachable workspace of a class of planar two-degree-of-freedom (dof) end-effector-type manipulators. This class is based on six planar linkages with five links and five joints, revolute and/or prismatic. A common set of two quadratic equations is presented that determine the workspace of all the class as a function of the input motions of the manipulator under study. The quadratic equations involve only the Cartesian coordinates (x,y) of the operation point. Thus, the formulation is governed by the analytical solution of a well known second order equation and the inverse kinematic problem is not required. Because of the simplicity of the involved equations, an algorithm can be easily implemented on a computer program. Examples of generated workspaces for all the class are given to illustrate the proposed approach. (C) 1999 Elsevier Science Ltd. All rights reserved.