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

• Published in: Mechanism and machine theory Vol. 34; no. 7; pp. 1057 - 1073
• Main Authors: Cervantes-Sánchez, J.J., Rendón-Sánchez, J.G.
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier Ltd 01.10.1999; New York, NY Elsevier
• Subjects: Applied sciences; Drives; Exact sciences and technology; Linkage mechanisms, cams; Mechanical engineering. Machine design; Planar mechanism; Parallel system; System with two degrees of freedom; Kinematics; Linkage mechanism; Modeling; Quadratic equation; Robotics; Manipulator; Inverse problem; Workspace
• ISSN: 0094-114X; 1873-3999
• DOI: 10.1016/S0094-114X(98)00077-9

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.