Patterned Bootstrap: A New Method Which Gives Efficiency for Precision Position Synthesis of Planar Linkages Available to Purchase

This paper presents a new method, termed as patterned bootstrap (PB), which is suitable for precision position synthesis of planar linkages. The method solves a determined system of equations using a new bootstrapping strategy. In principle, a randomly generated starting point is advanced to a final solution through solving a number of intermediate systems. The structure and the associated parameters of each intermediate system is defined as a pattern. In practice, a PB procedure generally consists of two levels: an upper level which controls the transition of patterns, and a lower level which solves intermediate systems using globally convergent root-finding algorithms. Besides introducing the new method, tunnelling functions have been added to several systems of polynomials derived by formal researchers in order to exclude degenerated solutions. Our numerical experiments demonstrate that many precision position synthesis problems can be solved efficiently without resorting to time-consuming polynomial homotopy continuation methods or interval methods. Finding over 95 percentages of the complete solutions of the 11 precision position function generation problem of a Stephenson-III linkage has been achieved for the first time.