On the coupler curve of 3R2C linkages

H. S. Yan, W. H. Hsieh

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


The purpose of this paper is to investigate the properties of the coupler curves generated by all 3R2C linkages. First, the 3x3 matrix with dual elements is used to derive the loop closure equation, the displacement equations are derived, and all joints variables are expressed in terms of input and output variables. Then, the parametric equations of the coupler curve are found by the D-H matrix. Finally, homogeneous coordinate is introduced to those displacement equations, and the order and some critical properties of the coupler curve are investigated based on the theories of algebraic curve and analytical geometry of three dimensions. In addition, RCRCR and RRCCR linkages are used as examples for illustration. Moreover, the results on the application of dimensional synthesis are discussed.

Original languageEnglish
Pages (from-to)251-267
Number of pages17
JournalTransactions of the Canadian Society for Mechanical Engineering
Issue number3
Publication statusPublished - 1998

All Science Journal Classification (ASJC) codes

  • Mechanical Engineering


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