Kinetostatics of Serial Robots
Kinetostatics is understood here as the study of the interplay between the feasible twists of and the constraint wrenches acting on the various rigid bodies of a mechanical system, when the system moves under static, conservative conditions. The feasible
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Kinetostatics of Serial Robots
5.1 Introduction Kinetostatics is understood here as the study of the interplay between the feasible twists of and the constraint wrenches acting on the various rigid bodies of a mechanical system, when the system moves under static, conservative conditions. The feasible twists of the various rigid bodies, or links, are those allowed by the constraints imposed by the robot joints. The constraint wrenches are, in turn, the reaction forces and moments exerted on a link by the links to which that link is coupled by means of joints. The subject of this chapter is the kinetostatics of serial robots, with focus on six-axis manipulators. By virtue of the duality between the kinematic and the static relations in the mechanics of rigid bodies, as outlined in Sect. 3.7, the derivation of the kinematic relations is discussed in detail, the static relations following from the former. We derive first the relation between the twist of the robot EE and the set of joint rates, which is given by a linear transformation induced by the robot Jacobian matrix. Once the foregoing relation is established for a general six-joint robot, the relation between the static wrench exerted by the environment on the EE and the balancing joint torques is derived by duality. Special robotic architectures are given due attention. Decoupled and planar architectures are treated as special cases of six-joint robots. The fundamental problem of singularities arising from a singular robot Jacobian in decoupled manipulators is given due attention as well. Two types of singularities are discussed here for the regional structure of decoupled robots. As a follow-up to the singularity analysis of this structure, its three-dimensional workspace is derived. An algorithm is proposed for the display of this workspace as pertaining to general regional structures whose inverse displacement analysis leads to a quartic polynomial.
Electronic supplementary material The online version of this article (doi: 10.1007/978-3-31901851-5_5) contains supplementary material, which is available to authorized users. J. Angeles, Fundamentals of Robotic Mechanical Systems: Theory, Methods, and Algorithms, Mechanical Engineering Series 124, DOI 10.1007/978-3-319-01851-5__5, © Springer International Publishing Switzerland 2014
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5 Kinetostatics of Serial Robots
The chapter closes with a section on kinetostatic performance indices. The purpose of these indices is twofold: They are needed in robot design to help the designer best dimension the links of the robot in the early stages of the design process, prior to the elastostatic and the elastodynamic design stages. These indices are also needed in the control of a given robot to ensure an acceptable kinetostatic performance under feedback control. One third, pragmatic application of these indices is the comparison of various candidate robots when a robotic facility is being planned. Elastostatic design pertains to the structural design of a robot to ensure that the links and the joint mechanic
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