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The article presents a general method for the elastodynamic analysis of planar mechanisms. It uses planar actual finite line elements (regular and irregular elements given in a companion article) and lumped mass systems to formulate the equations of motion of a mechanism. Damping coefficient matrix can incorporate time dependent viscous or coulomb damping coefficients in addition to the coefficients of velocity dependent internal damping. The forcing vector can incorporate any externally applied time dependent force or torque, inertial forces and inertial torques, any nonlinear viscous or Coulomb damping forces and torques. The matrix exponential method is introduced for the numerical solution of the equations of motion. Matrix displacement method of determining dynamic stresses using the generalized coordinate displacements is given. Elastodynamic analysis of a plane four-bar mechanism is performed for several cycles of kinematic motion, and the dynamic stresses are compared with those obtained by experiments. The method of “Critical-Geometry-Kineto-Elasto-Statics” (CGKES) is proposed for the computation of dynamic stress magnitudes making use of the critical geometry of the mechanism. It requires the analysis of a mechanism at the critical geometry position of the mechanism which is defined by the lowest fundamental frequency of the mechanism. The results predicted by the method of CGKES compares within two percent with the experimental results.

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SummaryThe Space Station Alpha is the most significant international space project of this century and the largest international technology development project ever undertaken. The space robot manipulators will be a substantial part of the space station and will perform tasks such as assembly as well as maintenance of the station. Therefore the robot manipulators need a very sophisticated real-time control capability for gross and fine motions (i.e. compliant motions) during various operations. Moreover, the proposed dual-arm robot system servicing the Space Station requires automated motion coordination, synchronization of the arms, and controlled mechanical interaction with fixed and moving objects involved in various tasks.