Abstract
The coupler-curve synthesis of four-bar linkages is a fundamental problem in kinematics. According to the Roberts-Chebyshev theorem, three cognate linkages can generate the same coupler curve. While the problem of linkage synthesis for coupler-curve generation is determined, it has been regarded as overdetermined, given that the number of coefficients in an algebraic coupler-curve equation exceeds that of linkage parameters available. In this paper, we develop a new formulation of the synthesis problem, whereby the linkage parameters are determined "exactly", within unavoidable roundoff error. A system of coupler-curve coefficient equations is derived, with as many equations as unknowns. The system is thus determined, which leads to exact solutions for the linkage parameters. A method of linkage synthesis from a known coupler-curve equation is further developed to find the three cognate mechanisms predicted by the Roberts-Chebyshev theorem. An example is included to demonstrate the method.
Original language | English |
---|---|
Journal | Mechanism and Machine Theory |
Volume | 94 |
Pages (from-to) | 177-187 |
Number of pages | 11 |
ISSN | 0094-114X |
DOIs | |
Publication status | Published - 5 Dec 2015 |
Keywords
- Algebraic equation of coupler curves
- Cognate linkages
- Four-bar linkage synthesis
- Path synthesis