Advances in Robot Kinematics: Analysis and Design by Michele Conconi, Marco Carricato (auth.), Jadran Lenarčič,

By Michele Conconi, Marco Carricato (auth.), Jadran Lenarčič, Philippe Wenger (eds.)

This e-book offers the newest learn advances within the idea, layout, keep watch over and alertness of robotic structures, that are meant for numerous reasons equivalent to manipulation, production, automation, surgical procedure, locomotion and biomechanics. the problems addressed are essentially kinematic in nature, together with synthesis, calibration, redundancy, strength keep an eye on, dexterity, inverse and ahead kinematics, kinematic singularities, in addition to over-constrained platforms. equipment used comprise line geometry, quaternion algebra, screw algebra and linear algebra. those equipment are utilized to either parallel and serial multi-degree-of-freedom systems.

The ebook comprises forty eight independently reviewed papers of researchers specialising in robotic kinematics. The members are the main recognized scientists during this sector. The papers were subdivided into the subsequent sections: Singularity research of parallel manipulators, layout of robots and mechanisms, movement making plans and mobility, functionality and homes of mechanisms, degree and calibration, Kinematic research and workspace.

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3 Summary From the previous sections, it is learned that there may be infinite solutions, a double solution or two distinct solutions to the forward kinematics for different cases of inputs. In this section, the above results will be summarized. Geometric characteristics for different cases will also be revealed. From brevity, Ai Bi⊥ is used to represent the perpendicular to Ai Bi passing through Ai , and circumcircle A is used to denote the circumcircle of points A1 , A2 and A3 . 1. Equations (7) and (31) are satisfied (Case 2a).

Constraint Singularities and the Structural Parameters of Parallel Robots 27 Fig. 2 Two solutions of 3-UPU parallel mechanisms with constraint singularities. 4 Conclusions Constraint singularities are used to characterize the configuration of lower mobility parallel manipulators in which both the connectivity of the moving platform and the mobility of the parallel mechanism increase their instantaneous values. In this paper, we have explained the nature of these singularities, by using the new formulae of mobility, connectivity, overconstraint and redundancy of parallel robots, recently proposed by the author, and we have demonstrate the relation between these singularities and the structural parameters of the parallel robots.

27). Expanding Eq. (27) leads to an algebraic equation in terms of the five joint variables of the RRPRR leg (all joint screws of the parallel manipulator are expressed as functions of these five variables). The solutions of this equation give the singular configuration of the manipulator. The expanded equation is not listed here because of the limited space. Several singular configurations have been identified. Two types of singular configurations are shown in Figure 4. The uncontrollable motion of the moving platform for the first singular configuration (Figure 4a) is a pure rotation, which axis intersects all four legs, is parallel to Geometric Algebra Approach to Singularity of Parallel Manipulators 47 Fig.

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