In forward dynamics problems, the applied forces on a machine or a mechanism are given and we want to calculate the resulting motion. In Chap. 13 , the inverse planar dynamic problems are introduced in which the desired motion of a machine or mechanism is known and we are looking for compatible forces and moments that can generate that motion. The inverse dynamics analysis is necessary for choosing suitable motors and actuators when the required motion is known. The connecting link between motion, forces, and moments is Newton’s second law and through finding the acceleration terms. The calculated dynamic forces and moments that are needed to generate the desired motion are compared with the corresponding static ones and used as a means for verification of the obtained results. It is shown how static solutions can provide approximations for dynamic solutions in cases where inertia effects are not significant (low mass times acceleration). Finally, application of matrix algebra for solving systems of equations of static equilibrium (in statics) or equations of dynamic equilibrium (in dynamics) is illustrated.

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Inverse Planar Dynamics

  • Mehrdaad Ghorashi

摘要

In forward dynamics problems, the applied forces on a machine or a mechanism are given and we want to calculate the resulting motion. In Chap. 13 , the inverse planar dynamic problems are introduced in which the desired motion of a machine or mechanism is known and we are looking for compatible forces and moments that can generate that motion. The inverse dynamics analysis is necessary for choosing suitable motors and actuators when the required motion is known. The connecting link between motion, forces, and moments is Newton’s second law and through finding the acceleration terms. The calculated dynamic forces and moments that are needed to generate the desired motion are compared with the corresponding static ones and used as a means for verification of the obtained results. It is shown how static solutions can provide approximations for dynamic solutions in cases where inertia effects are not significant (low mass times acceleration). Finally, application of matrix algebra for solving systems of equations of static equilibrium (in statics) or equations of dynamic equilibrium (in dynamics) is illustrated.