Burmester’s solution to the problem of guiding a body through four precision points has been extended to find planar mechanisms that have their pivots located inside prescribed regions. The complex number formulation has been used to generate the Burmester curves. A random search technique was developed to choose a new set of precision points that lie within user specified limits, in order to find a set of curves that pass through the desired regions. A computer program was written to generate Burmester curves that lie within the desired regions, while maintaining a coupler motion within satisfactory limits. An automobile suspension linkage was successfully designed using this program.
A general closed-form approach to the solution of loop equations of planar n-bar linkages is presented. Each loop of a set of canonical independent loops is decomposed to a set of vectors. Several common combinations of revolute and prismatic joints are defined. By evaluating the types of joints at each end of a vector, the magnitude and direction of the vector are determined to be known constants or unknown variables. This leads to an identification of the number of unknowns and the distribution of unknowns in the loop. This identification allows the unknowns to be found by matching the situation to one of the unique, closed-form cases for a solvable loop. A computer software application has been developed and is analyzed for efficiency.
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