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Numerical algebraic geometry is the field that studies the computation and manipulation of the solution sets of systems of polynomial equations. The goal of this work is to formulate spatial mechanism analysis and design problems via a method suited to employ the tools of numerical algebraic geometry. Specifically, equations are developed using dual special unitary matrices that naturally use complex numbers to express physical and joint parameters in a mechanical system. Unknown parameters expressed as complex numbers readily admit solution by the methods of numerical algebraic geometry. This work illustrates their use by analyzing the spatial RCCC and RRRCC linkages. The specialization to pure rotations using special unitary matrices is also presented and used in the analysis of the spherical four-bar and Watt I linkages. The motion curves generated in this work are validated by comparison to other published work.
Andrew P Murray, David H Myszka
Primary Advisor's Department
Mechanical & Aerospace Engineering
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Almestiri, Saleh M., "Spatial Mechanism Analysis and Synthesis by Dual Special Unitary Matrices" (2016). Stander Symposium Posters. 743.
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