Multibody system kinematic analysis

Physical motion is common to most situations in which the human functions and is therefore fundamental to the analysis of performance. Parameters such as segment position, orientation, velocity, and acceleration are derived using kinematic or dynamic analysis or both. This approach is equally appropriate for operations on a single joint system or linked multibody systems, such as is typically required for human analysis. Depending on the desired output, foreword (direct) or inverse analysis may be employed to obtain the parameters of interest. For example, inverse dynamic analysis can provide joint torque, given motion and force data while foreword (direct) dynamic analysis uses joint torque to derive motion. Especially for three-dimensional analyses of multijoint systems, the methods are quite complex and are presently a focal point for computer implementation [Allard et al., 1994]. 

In general, the equations of motion are nonlinear. Making special assumptions on the MBS under consideration some multibody formalisms result in partially linear equations. For example the kinematics can be assumed to be linear in some applications of vehicle dynamics If the motion of a railway vehicle on a track is considered, the deviation of the vehicle from the nominal motion defined by the track can be assumed to be so small that one can linearize around that nominal motion. If in addition also the forces are linear, the resulting equations of motion are linear. For a straight line track and linear, time independent force laws the equations are linear with constant coefficients. For details on multibody formalisms which establish linear or partially linear equations, the reader is referred to [Wal89]. In this section we will assume that the equations of motion are given in a nonlinear form and we will show how the linearized equations look like. In subsequent chapters we will refer then to the linear equations when discussing linear system analysis methods. 

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See also in sourсe #XX -- [ ]

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