Position analysis of seven-link Barranov truss based on conformal geometric algebra
The position analysis of mechanism is the basis of kinematics and dynamics research of mechanism.A conformal geometric algebraic(CGA)method for position analysis of seven-link Barranov truss is proposed to solve the problems of the traditional mechanism position analysis theory,such as the complicated operation of rotating coordinate transformation matrix and the difficulty of solving multivariate nonlinear equations of higher order.The expression of position coordinates of each moving point is established by means of translation,rotation operator and geometric formula expression in CGA.According to the properties of inner product geometry in CGA,the 16-degree position input-output equation of the mechanism and all its solutions are obtained directly.After all the solutions of the higher order equation are substituted back,the position coordinates of all moving points can be obtained.Finally,the effectiveness of the new method is verified by numerical examples.The results show that the geometric intuitionicity of the proposed algorithm is significantly superior to the traditional complex vector method and D-H matrix method.The proposed algorithm can not only avoid matrix operations and elimination operations,but also solve without adding or missing roots.
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