Graduate Thesis Or Dissertation
 

Derivation and automatic generation of Kane's dynamical equations for mechanical manipulators

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https://ir.library.oregonstate.edu/concern/graduate_thesis_or_dissertations/r494vn46c

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  • To design and precisely control a manipulator requires developing an efficient dynamic model of the system. The present work demonstrates how this can be accomplished by employing Kane's dynamical equations. First, a detailed manual derivation of the equations of motion for a particular robot is presented in such way that each step in the analysis serves as an example for the derivation of the dynamic equations for serial manipulators in general. Discussions are given regarding the merits of using different sets of generalized speeds. Based on this formulation procedure, an algorithm is presented, which enables computers to automatically generate and integrate Kane's dynamical equations of motion for mechanical manipulators, or to calculate the torques and/or forces required to carry out a user-specified motion of the manipulator. Applicable to nearly any manipulator, the algorithm uses recursive computations of angular velocities, velocities, generalized inertia forces and generalized active forces. To save computation time, all ingredients for formulating the equations of motion are expressed in scalar forms. The resulting equations contain no approximations beyond the assumptions that the links are rigid and perfectly connected. As an example, simulation results of both manually-derived and automatically-generated equations for the Intelledex 605 Robot arm are reported and it is shown that the algorithm is more efficient than those in the listed literature.
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