Abstract

The high fidelity modeling of robotic systems is addressed. The operation of a robot usually consists of a free-flight regime, a contact/impact regime, and a constrained motion regime. Presented in this paper is a demonstration of a systematic method for modeling the complete motion of a manipulator. The model is complete in the sense that all motion regimes are seamlessly handled and the inherently distributed nature of elasticity and mass are rigorously modeled. Since the model properly integrates the distributed parameters with the discrete parameters (boundary conditions too), the effects of disturbance waves propagating in the robotic chain of bodies can be studied.

The methodology demonstrated in this work is a recent development. The methodology is based in variational principles but its operational aspects hide the variational calculus. The method seamlessly handles holonomic and nonholonomic motion constraints. The method also allows the determination of post impact velocities and pointwise velocity fields for hybrid parameter multiple body (HPMB) systems. Exact relationships used to determine when the separation of colliding bodies has occurred are also readily generated. For analysts familiar with Kane’s form of the Gibbs-Appell equations, the method will be affable.

The system modeled in this paper will allow all the curious HPMB system dynamics to be studied. That is: a two flexible link planar manipulator undergoing all three motion regimes mentioned above. The flexible beams are taken as Euler-Bernoulli beams with large deflections. The modeling technique will be demonstrated by deriving the complete model of this system.

Some of the advantages of the technique demonstrated herein include: a) closed form hybrid parameter models, b) automatic boundary conditions, c) holonomic and nonholonomic motion, d) wave propagation, and e) rapid regeneration of system models.

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