Advances in Robot Kinematics: Mechanisms and Motion by Jadran Lenarcic, B. Roth

By Jadran Lenarcic, B. Roth

This booklet offers the latest study advances within the conception, layout, keep an eye on and alertness of robot platforms, that are meant for various reasons resembling manipulation, production, automation, surgical procedure, locomotion and biomechanics. the problems addressed are essentially kinematic in nature, together with synthesis, calibration, redundancy, strength regulate, dexterity, inverse and ahead kinematics, kinematic singularities, in addition to over-constrained structures. tools used contain line geometry, quaternion algebra, screw algebra, and linear algebra. those equipment are utilized to either parallel and serial multi-degree-of-freedom platforms.

The booklet contains fifty three independently reviewed papers of researchers specialising in robotic kinematics. The members are the main recognized scientists during this region. The papers were subdivided into the next sections: equipment in Kinematics, homes of Mechanisms, Humanoids and Biomedicine, research of Mechanisms, Workspace and function, layout of Mechanisms, movement Synthesis and Mobility.

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2. A Singularity Detection Scheme This singularity detection problem has been addressed in [Merlet 01] where an efficient algorithm was exhibited. This algorithm proceeds along the following steps: symbolic computation is used to determine an analytical form of the determinant of J−1 and its sign at a particular pose X1 . Then an interval analysis based method [Jaulin 01; Moore 79], that takes round-off errors into account, allows one to determine if the motion variety includes a set of poses in which the determinant has a sign opposite to the one found at X1 .

1. Although these problems have already been solved in the literature by ad-hoc algorithms, they could be also worked out by determining all 3 × 3 rotation matrices satisfying three linear conditions in the direction cosines. In this respect, the procedure proposed in this paper is a viable alternative to already-known solving methods. Figure 1a shows a fully- parallel spherical wrist, whose direct kinematics aims at determining all possible orientations of the moving platform 25 Determining the 3×3 Rotation Matrics for a given set of actuator lengths (Innocenti and Parenti-Castelli, 1993).

1, pp. 4–17. , and Shoham, M. (2003), Investigations of Parallel Manipulators Using Linear Complex Approximation, Journal of Mechanical Design, vol. 125, pp. 564–572. Yoshikawa, T. (1985), Manipulability of Robotic Mechanisms, Int. J. of Robotics Research, vol. 4, no. 2, pp. 3–9. , and Angeles, J. (1997), Kinematic Isotropy and the Optimum Design of Parallel Manipulators, Int. J. of Robotics Research, vol. 16, no. 2, pp. 185–197. it Abstract The paper presents a solution to all the spatial kinematics problems that require determination of the 3 × 3 rotation matrices whose nine direction cosines satisfy three linear equations.

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