Resonant Robotic Systems
Especially designed as self-sustaining oscillating systems, resonant robotic systems use the natural modes of oscillation of electromechanical modules for their movements. In fact, manipulator systems built on these principles demonstrate record-breaking
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§2.1 Equations of motion for reSOIlant robots 2.1.1. In robotics, as in theoretical mechanics [78], there are two problems to be solved in robot dynamics [35, 67]. The fIrst, which is equivalent to the inverse (fIrst) problem of dynamics, assumes specifIc motions for the robot components (kinematic equations of motion); it is required to fInd the motive forces (either moments or direct forces), which cause the actual motion. In order to do this the dynamic forces in the drives and kinematic pairs must also be calculated. The solution of the inverse problem in dynamics makes it possible to match the choice of actuator driver and to calculate the required strength characteristics of the drive elements and robot components. The second problem in robot dynamics, similar to the direct problem of dynarnics in theoretical mechanics, consists of defIning the actual motion of a manipulator (deviations from the programmed motion) due to the given parameters of the mechanical system and controls. In the majority of cases when studying resonant robotic systems it is necessary to solve the fIrst problem of dynamics. This arises because resonant robots were applied mainly to transport devices used in production processes to transfer products held by grippers from one position in the workspace to another, possibJy including re-orientation. In this case the operating speed and positional accuracy gare of primary importance, no matter what precision in the trajectory is required. In cyclic resonant robots motion is usually provided successively by drives for each degree of freedom. As a result, the form of the gripper trajectory is completely defmed by the foml of the kinematic pairs (sliding or rotational), which occur in the basic kinematic scheme of the manipulator. The accuracy with which these the trajectories are followed is determined by the accuracy of manufacture of the kinematic pairs. Moreover, there is little deviation in the operating motion of resonant mechanical systems from their natural (programmed) motion if an appropriate mechanical energy store is chosen. Drive actuators playa subsidiary role in producing programmed motion, providing compensation for the energy expended on friction and to perform active work. As a result, the problem of dynamics leads to the choice of control actions to produce the manipulator motion within defIned limits or with the required behaviour. The conditions for motion can be various restraints (kinematic, geometric or energy limitations, etc.) imposed on the drive or on the manipulator elements. The provision of motion with the required behaviour can be expressed as satisfying the requirements of the motion parameters (speed, smoothness, freedom from impact, etc.) and control (energy expenditure, smoothness, heat
V. I. Babitsky et al., Resonant Robotic Systems © Springer-Verlag Berlin Heidelberg 2003
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Chapter 2. Dynamics of resonant robotic systems --------
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generation in the drive, etc.). The choice of control can be made from engineering considerations taking into
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