Motor -network techniques for multibody dynamic systems.

摘要

A new approach to the equations formulation for three-dimensional multibody dynamic systems with kinematic loops is presented. Its most prominent feature is that it extends the graph-theoretic technique for multibody dynamic systems to utilize mathematical analog screws, twists, wrenches, dual-vectors, and Plucker coordinates. The new approach system graph could be obtained from the system rotational graph by the principle of transference where each edge of the rotational graph is replaced by a motor representing the twist and the wrench of the corresponding physical element. The system motor-network graph is thus simple and the motion equation formulation procedures, which utilize motor algebra rather than vector algebra, is compact, direct and systematic.;The validity of twists and wrenches as across and through variables for the motor-network techniques presented in this thesis is demonstrated philosophically, mathematically, and with general examples. The new approach preserves the methodical nature of the traditional linear graph theoretical method. The similarity between the vector-network techniques using vector algebra and the new motor-network techniques using motor algebra is demonstrated by examples utilizing joint and body coordinates.;New dual-vector variables and dual-expressions are developed. They include single-row dual-Jacobian matrices for joints with single and multiple axes, and node-to-node dual-transformation matrices required for transforming twists and wrenches from their perspective frame to a common frame. These dual-transformation matrices, which are analogous to the homogenous transformation matrices, are used to produce an overloaded cutset matrix the elements of which are dual-transformation matrices rather than zeros and ones. This matrix is orthogonal to the similarly overloaded system circuit matrix and it is called by the author the "system geometrical cutset matrix". This geometrical cutset matrix when post multiplied, using motor algebra, by the system wrenches produces the system dual-cutset equations. In case of joint coordinate formulation each cutset equation is projected onto the motion space of the corresponding branch joint to obtain scalar second order differential equations free from the branch joint constraint force and moment.;A symbolic computer program called "MoNet" (acronym for motor-network technique) is developed for the automatic generation of motion equations in relative coordinates to demonstrate the robustness of this technique. From the description of a dynamic system the program formulates a column matrix of the system wrenches, constructs the system geometrical cutset matrix, and assembles a diagonal matrix using branch joints twist-based local dual-Jacobians. The system scalar differential equations are the result of multiplying these three matrices using motor algebra. Similarly, the system scalar constraint equations, for closed-loop systems, are the result of multiplying three matrices: a column matrix of the system twists, the transpose of the system geometrical cutset matrix, and a diagonal matrix assembled from the chord joint wrench-based local dual-Jacobians.