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Volume 9, issue 2 | Copyright
Mech. Sci., 9, 297-305, 2018
https://doi.org/10.5194/ms-9-297-2018
© Author(s) 2018. This work is distributed under
the Creative Commons Attribution 4.0 License.

Research article 24 Sep 2018

Research article | 24 Sep 2018

Solution Region Synthesis Methodology of RCCC Linkages for Four Poses

Jianyou Han and Yang Cao Jianyou Han and Yang Cao
  • School of Mechanical Engineering, University of Science and Technology Beijing, Beijing 100083, China

Abstract. This paper presents a synthesis methodology of RCCC linkages based on the solution region methodology, R denoting a revolute joint and C denoting a cylindrical joint. The RCCC linkage is usually synthesized via its two defining dyads, RC and CC. For the four poses problem, there are double infinite solutions of the CC dyad, but there is no solution for the RC dyad. However, if a condition is imposed that leads to a coupling of the two dyads, a maximum of four poses can be visited with the RCCC linkage. Unfortunately, until now, there is no methodology to synthesize the RCCC linkage for four given poses besides optimization method. According to the coupling condition above, infinite exact solutions of RCCC linkages can be obtained. For displaying these RCCC linkages, we first build a spherical 4R linkage solution region. Then solutions with circuit and branch defects can be eliminated on this solution region, so that the feasible solution region is obtained. An RCCC linkage can be obtained by using the prescribed spatial positions and selected a value on the feasible solution region. We take values on the feasible solution region by a certain step length and many exact solutions for RCCC linkages can be obtained. Finally we display these solutions on a map, this map is the solution region for RCCC linkages.

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The paper presents a solution region synthesis methodology for RCCC linkages. First, we couple the RC and CC dyads for obtaining all synthesis equations. Then using the solution region theory and Bertini software, all solutions for RCCC linkages can be obtained. The key contribution of this paper is that all solutions of RCCC linkages for four specific poses are obtained. Only one RCCC linkage can be synthesized by the methods published before;
The paper presents a solution region synthesis methodology for RCCC linkages. First, we couple...
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