Workspace Analysis of 2-PR(Pa)U- 2-PR(Pa)R New Parallel Mechanism

Document Type : Original Article


Department of Mechanical Engineering, University of Tabriz, Iran


Parallel kinematic machines, are closed loop structures which have more accuracy, stiffness and ability to withstand high loads. Kinematic of these mechanisms is complicated due to their closed–loop structure, parallel pods, joint constraints and movement constraints. This paper proposes a new parallel mechanism that has four degrees of freedom. In workspace analysis algorithm, conversion of inverse kinematics after providing the moving platform position (position and orientation) from search algorithm, provides basis position for testing the physical limitations of machine. Workspace of the mechanism is obtained by extracting analytical relations and consequently computational programs are written in MATLAB software. Sweep operations is started by dividing the workspace into x – y planes or horizontal sections with fixed spaces of z, then after sweeping all points of the plane, sweep operations of the next plane begins. Constraints and physical limitations considered in this mechanism includes moving restriction of saddle, collision of basis to rails, joint angles and collision of basis to moving platform. If any of these limits are violated, considered point would not be considered in the workspace. Then, to evaluate the correctness of the obtained results of workspace analysis, a suggested mechanism is simulated in SolidWorks software and obtained workspace is validated in this study. Also position kinematic and workspace analysis results are verified experimentally.


[1]     Tsai, L., “Robot Analysis: the Mechanics of Serial and Parallel Manipulators”, WILEY, 1999.
[2]     Merlet, J. P., “Parallel Robots”, Kluwer academic publishers, 2001.
[3]     Wu, J., Yin, Z., “A Novel 4-DOF Parallel Manipulator H4”, Parallel Manipulators, Towards New Applications, No. April, 2008, pp. 405–448.
[4]     Conti, J. P., Clinton, C. M., Zhang G., and Wavering A. J., “Dynamic Variation of the Workspace of an Octahedral Hexapod Machine Tool During Machining”, the National Science Foundation, Engineering Research Center Program, the University of Maryland, Harvard University, and Industry, 1997.
[5]     Wang, Z., Liu, W., and Lei, Y., “A Study on Workspace, Boundary Workspace Analysis and Work Piece Positioning for Parallel Machine Tools”, Mechanism and Machine Theory, Vol. 36, No. 5, 2001, pp. 605–622.
[6]     Zhao, J. S., Chen, M., Zhou, K., Dong, J. X, and Feng, Z. J., “Workspace of Parallel Manipulators with Symmetric Identical Kinematic Chains”, Mechanism and Machine Theory, Vol. 41, No. 6, 2006, pp. 632–645.
[7]     Wang, Z., Ji, S., Li, Y., and Wan, Y., “A Unified Algorithm to Determine the Reachable and Dexterous Workspace of Parallel Manipulators”, Robotics and Computer-Integrated Manufacturing, Vol. 26, No. 5, 2010, pp. 454–460.
[8]     Brisan, C., Csiszar, A., “Computation and Analysis of the Workspace of a Reconfigurable Parallel Robotic System”, Mechanism and Machine Theory, Vol. 46, No. 11, 2011, pp. 1647–1668.
[9]     Liu, X.-J., Wang, J., “Some New Parallel Mechanisms Containing the Planar Four-Bar Parallelogram”, The International Journal of Robotics Research, Vol. 22, No. 9, 2003, pp. 717–732.