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This work seeks to efficiently and systematically model and solve the equations associated with the class of design problems arising in the study of spherical kinematics. To accomplish this, the group of special unitary matrices, SU(2), is utilized. SU(2) is used to analyze and synthesize the kinematics of a variety of systems including the three-roll wrist, the spherical four-bar mechanism, and the spherical Watt I linkage. Two methods of formulating the synthesis problem are considered. Specifically, the five orientation synthesis of a spherical four-bar mechanism and the eight orientation task of the Watt I linkage are solved using both the loop closure equations and an approach derived from the dot product that recognizes physical constraints within the linkage. Finally, using SU(2) readily allows for the use of a homotopy-continuation-based solver, in this case Bertini. The use of Bertini is motivated by its capacity to calculate every solution to a design problem.
Andrew P Murray, Dave Harry Myszka
Primary Advisor's Department
Mechanical and Aerospace Engineering
Stander Symposium poster
"Displacement Analysis and Rigid Body Guidance in Spherical Linkages Using SU(2) and Homotopy Continuation" (2018). Stander Symposium Posters. 1298.