Abstract
This chapter formulates the synthesis equations for a Watt I six-bar linkage that moves through \(N\) specified task positions. For the maximum number of positions, \(N=8\), the resulting polynomial system consists of 28 equations in 28 unknowns, which can be separated into a nine sets of variables yielding a nine-homogeneous Bezout degree of \(3.43\times 10^{10}\). We verify these synthesis equations by finding isolated solutions via Newton’s method, but a complete solution for \(N=8\) seems beyond the capability of current homotopy solvers. We present a complete solution for \(N=6\) positions with both ground pivots specified.
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Plecnik, M., McCarthy, J.M., Wampler, C.W. (2014). Kinematic Synthesis of a Watt I Six-Bar Linkage for Body Guidance. In: Lenarčič, J., Khatib, O. (eds) Advances in Robot Kinematics. Springer, Cham. https://doi.org/10.1007/978-3-319-06698-1_33
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DOI: https://doi.org/10.1007/978-3-319-06698-1_33
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