In this paper, we present a new algebraic elimination algorithm for the inverse static force analysis of a special planar three-spring system. The system consists of three linear springs joined to the ground at the two fixed pivots and connected to the two moving pivots at the platform. When exerted by specified static force, the goal of inverse static analysis is to determine all the equilibrium configurations. First of all, a system of seven polynomial equations in seven variables is established based on the geometric constraint and static force balancing. Then, four basic constraint equations in four variables are obtained by variable substitution. Next, a 20 by 20 resultant matrix is reduced by means of three consecutive Sylvester elimination process. Finally, a 54th-degree univariate polynomial equation is directly derived without extraneous roots in the computer algebra system Mathematica 9.0. At last, a numerical example is given to verify the elimination procedure.
- Design Engineering Division
- Computers and Information in Engineering Division
A New Algebraic Solution to Inverse Static Force Analysis of a Special Planar Three-Spring System
Zhang, Y, Liao, Q, Wei, S, Wei, F, & Li, D. "A New Algebraic Solution to Inverse Static Force Analysis of a Special Planar Three-Spring System." Proceedings of the ASME 2016 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. Volume 5B: 40th Mechanisms and Robotics Conference. Charlotte, North Carolina, USA. August 21–24, 2016. V05BT07A041. ASME. https://doi.org/10.1115/DETC2016-59790
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