A simplified approach for obtaining the workspace of a class of 2-dof planar parallel manipulators - Cervantes-Sánchez, J.J.; Rendón-Sánchez, J.G. (Mechanism and machine theory, 1999)
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.