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Workspace analytic determination of two similar translational parallel manipulators

Published online by Cambridge University Press:  02 March 2021

Raffaele Di Gregorio  and
Roberto Zanforlin
Raffaele Di Gregorio*
Affiliation:
Department of Engineering, University of Ferrara, Via Saragat, 1; 44100 Ferrara (Italy)
Roberto Zanforlin
Affiliation:
Department of Engineering, University of Ferrara, Via Saragat, 1; 44100 Ferrara (Italy)
*
Email: rdigregorio@ing.unife.it.
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Summary

The design of a parallel manipulator for a given workspace would be greatly facilitated, if the analytic expressions of the hypersurfaces bounding the workspace were available. In translational parallel manipulators (TPMs), the hypersurfaces bounding the workspace are actually threedimensional surfaces, which are the geometric locus of all the positions assumed by an end-effector point when the TPM reaches the workspace borders. These surfaces can be represented in a Cartesian reference system fixed to the frame. This paper studies the workspace of two TPMs, that have the same closure equations and workspace when a few geometric conditions are satisfied. The two TPMs are the translational 3-RUU and the DELTA robot. The kinematic analyses of these two TPMs are different from one another only when velocity and accelerations are considered. The result of this study is that the analytic expression of the surfaces bounding their workspace is a fourth degree polynomial equation, in the coordinates of a plattorm point, which contains all the manipulator geometric parameters. This analytic expression is given in an explicit form. The use of this expression is illustrated through a numerical example.

Keywords

ManipulatorsKinematicsPosition analysisWorkspace
Type
Research Article
Information
Robotica , Volume 21 , Issue 5 , October 2003 , pp. 555 - 565
Copyright
Copyright © Cambridge University Press 2003

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References

1. Wampler, C.W., “Forward displacement analysis of general six-in-parallel SPS (Stewart) platform manipulators using Soma coordinates”, Mechanism and Machine Theory 31(3), 331–337 (1996).Google Scholar
2. Husty, M.L., “An algorithm for solving the direct kinematics of the Stewart-Gough platform”, Mechanism and Machine Theory 31(4), 365–380 (1996).CrossRefGoogle Scholar
3. Innocenti, C., “Forward kinematics in polynomial form of the general Stewart platform”, ASME Journal of Mechanical Design 123(2), 254–260 (2001).CrossRefGoogle Scholar
4. Merlet, J.-P., “Singular configurations of parallel manipulators and Grassmann geometry”, Int. J. Robotics Research 8(5), 45–56 (1989).CrossRefGoogle Scholar
5. St-Onge, B.M. and Gosselin, C.M., “Singularity analysis and representation of the general Gough-Stewart platform”, Int. J. Robotics Research 19(3), 271–288 (2000).CrossRefGoogle Scholar
6. Di Gregorio, R., “Singularity-Locus expression of a class of parallel mechanisms”, Robotica 20(3), 323–328 (2002).CrossRefGoogle Scholar
7. Gosselin, C.M., “Determination of the workspace of spatial 6-dof parallel manipulators”, ASME Journal of Mechanical Design 112(3), 331–336 (1990).Google Scholar
8. Kohli, D. and Spanos, J., “Workspace analysis of mechanical manipulators using polynomial discriminants”, ASME Journal of Mechanisms, Transmissions, and Automation in Design 107, 209–215 (1985).CrossRefGoogle Scholar
9. Gupta, K.C. and Kazerounian, K., “Improved numerical solutions of the inverse kinematics of robots”, Proc. of IEEE Int. Conf. on Robotics and Automation, St-Louis, USA (1985) pp. 218–224.Google Scholar
10. Rastegar, J. and Deravi, P., “Methods to determine workspace, its subspaces with different numbers of configurations and all the possible configurations of a manipulator”, Mechanism and Machine Theory 22(4), 343–350 (1987).CrossRefGoogle Scholar
11. Di Gregorio, R., “Closed-Form Solution of the Position Analysis of the Pure Translational 3-RUU Parallel Mechanism”, Proc. of the 8th Symposium on Mechanisms and Mechanical Transmissions, MTM 2000, Timisoara, Romania (2000) Vol. 1, pp. 119–124.Google Scholar
12. Clavel, R., “DELTA, a fast robot with parallel geometry”, Proc. of the 18th International Symposium on Industrial Robots, Sydney, Australia (1988) pp. 91–100.Google Scholar
13. Pierrot, F., Reynaud, C. and Fournier, A., “DELTA: a simple and efficient parallel robot”, Robotica 8(1), 105–109 (1990).Google Scholar
14. Di Gregorio, R., “Rotation singularities in the DELTA-like manipulators”, Proc. of the ASME 2002 Design Engineering Technical Conferences and Computers and Information in Engineering Conference, DETC/CIE, 2002, Montreal, Canada (2002) Paper No. DETC2002/MECH-34264.Google Scholar