An algorithm has been created for the design of 5-SS linkages that reach 7 spatial task positions. 5-SS refers to the 5 spherical to spherical binary links that connect a moving platform to the fixed platform of these single degree of freedom mechanisms. Attached to that moving platform is an end effector frame. The goal of these motion generators is to move that end effector frame in a particular manner.
The algorithm consists of five main steps:
- Specification of task positions
- Generating new sets of task positions
- Synthesis of 5-SS mechanisms
- Analysis of mechanisms
- Evaluation of mechanism configurations
At the heart of the synthesis routine is the algebraic solution to the SS dyad equations. This system of 6 bilinear equations in 6 unknowns is solved with a generalized eigenvalue method. Formulation of these equations was introduced by Chen and Roth and an algebraic solution was given by Innocenti.
As an example design, the algorithm has been applied to the design of a steering linkage. The motion objective is to change the track, wheelbase, camber, and wheel height in a turn, while maintaining Ackermann geometry.
P. Chen, and B. Roth, 1969. “Design equations for the finitely and infinitesimally separated position synthesis of binary links and combined link chains,” Journal of Manufacturing Science and Engineering, 91(1): 209-219.
C. Innocenti, 1995. “Polynomial solution of the spatial Burmester problem,” Journal of Mechanical Design 117(1): 64-68.
M. Plecnik and J. M. McCarthy, 2012. “Design of a 5-SS spatial steering linkage,” Proceedings of the ASME 2013 IDETC/CIE Conference, Paper No. DETC2012-71405, August 12-15, 2012, Chicago, Illinois, USA.