Kinematic and dynamic analyses of spatial link mechanisms with closed kinematic structure

The proposed study is a further development of the matrix method applied to kinematic and dynamic problems of multi-loop spatial mechanisms. A mathematical model of a multi-loop spatial mechanism with multiple degrees of freedom using coordinate system transformation matrices is formulated. Two types of matrices, that is, constant link matrices and variable matrices of kinematic pairs are introduced. The methodology of solving closure equations describing a mechanism position is presented. Computer simulation based on the proposed methodology makes it possible to choose a rational scheme of the analyzed mechanism in the design phase. Since the closure condition is checked repeatedly, it needs to be simplified to reduce computational costs. This problem is solved by the matrix method in which constant and variable matrices are separated. An analytical description of the relative motion of links is presented using a linear transformation of the coordinate systems associated with the links. The mechanism under consideration contains independent closed kinematic chains or contours. Matrix equations of the contours are formulated and transformed into algebraic equations to be solved. The dynamic analysis of the system is based on the solution of the Lagrange and contour equations. The matrix method is efficient owing to the general analytical approach, which is independent of a particular form of the mechanism. Solving the analysis problem makes it possible to investigate the properties of the mechanism. The matrix method will be useful in studies of complex spatial designs, such as car suspension, aircraft landing gear with «leg breaking», etc.

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