Abstract
In this chapter we examine the kinematic synthesis theory for spatial serial chains. The kinematics equations of the chain are presented in their usual form using the Denavit-Hartenberg convention. The product of exponentials version of these kinematics equations are then reformulated using relative displacements from a reference position. These equations are shown to be equivalent to a dual quaternion, or Clifford algebra, formulation of the kinematics equations. It is these equations that are used for the design of serial chains. Remarkably, these equations specialize to the well-known complex vector design equations for planar serial chains. The complexity of the synthesis problem is known to simplify if the serial chain has a reachable surface, and we consider two cases the sphere and the circular torus. While the synthesis equations for the spatial SS chain has 20 solutions, the spatial RRS chain that generates the circular torus has over 90,000 solutions.
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Notes
- 1.
This chapter combines excerpts from J.M. McCarthy and G.S. Soh, Geometric Design of Linkages, Springer, 2010, and is based on the Ph.D. research by Alba Perez and Haijun Su. Reproduced by kind permission of Springer © 2012.
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McCarthy, J.M. (2013). Kinematic Synthesis. In: McCarthy, J. (eds) 21st Century Kinematics. Springer, London. https://doi.org/10.1007/978-1-4471-4510-3_2
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DOI: https://doi.org/10.1007/978-1-4471-4510-3_2
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