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

This publication offers the newest learn advances within the thought, layout, keep watch over and alertness of robotic structures, that are meant for various reasons comparable to 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. equipment used comprise line geometry, quaternion algebra, screw algebra and linear algebra. those tools are utilized to either parallel and serial multi-degree-of-freedom systems.

The e-book comprises forty eight independently reviewed papers of researchers specialising in robotic kinematics. The members are the main known scientists during this zone. The papers were subdivided into the next 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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Ben-Horin et al. 2 Singularity Equation The singularity analysis is performed using a coordinate-free invariant version of the Jacobian matrix determinant written in terms of GCA, which is suitable for robots of motion ruled by six pure forces, represented by six zero-pitch screws. This coordinate-free version of the Jacobian determinant was derived by McMillan and White (1991), after proposing a significantly larger expression by White (1983) eight years before. A paradigm of robots ruled by six pure forces is the general GSP.

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. 4 Singular configurations of the 5-dof parallel manipulator. two R joint axes of the RRPRR leg and perpendicular to P joint axis of the RRPRR leg. In the second singular configuration (Figure 4b) the uncontrollable motion is a general screw motion.

The Grassmann–Cayley algebra was employed in Staffetti and Thomas (2000) and Ben-Horin and Shoham (2006). The Clifford algebra was used in Collins and McCarthy (1998) and Selig (2000). In Zamora-Esquivel and Bayro-Corrochano (2006) and in Tanev (2006) the geometric algebra was applied. The Grassmann and Clifford algebras were created in the 19th century. In the second half of the 20th century Clifford algebras have been “rediscovered” and further developed into a unified language named “geometric algebra” in Hestenes (1999), Lasenby et al.

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