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

This publication offers the latest study advances within the thought, layout, keep an eye on and alertness of robotic platforms, that are meant for quite a few 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. tools used contain line geometry, quaternion algebra, screw algebra and linear algebra. those tools are utilized to either parallel and serial multi-degree-of-freedom systems.

The ebook contains forty eight independently reviewed papers of researchers specialising in robotic kinematics. The members are the main regarded scientists during this region. 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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**Sample text**

32) into the ﬁrst equation of (3), we have sin(φ − θ1 − 2π/3) = − sin(θ1 + 2π/3) (33) which leads two solutions if θ1 = −π/6 and 5π/6: φ=0 (34) φ = 2θ1 + π/3 (35) or a double solution if θ1 = −π/6 or 5π/6: φ = 0. (36) 36 X. 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.

And Duffy, J. (1996), An application of screw algebra to the acceleration analysis of serial chains, Mechanism and Machine Theory 31(4), 445–457. M. (2000), Clifford algebra of points, lines and planes, Robotica 18, 545–556. Staffetti, E. and Thomas, F. (2000), Analysis of rigid body interactions for compliant motion tasks using the Grassmann-Cayley algebra, in Proceedings IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2000), Vol. 3, pp. 2325–2332. K. (2006), Singularity analysis of a 4-dof parallel manipulator using geometric algebra, in Advances in Robot Kinematics, Mechanism and Motion, Lenarˇciˇc, J.

Our approach is as follows. First, we assume that if a point appears more than once in each monomial, then each appearance belongs to a different geometric entity. Each monomial has three brackets, each bracket containing four points, thus 12 points are part of geometric entities that have to be identiﬁed. From the deﬁnition of the meet operation (Eq. (2)), to obtain a monomial of brackets of four points the geometric entities involved may be 2- or 3-extensors (lines or planes). Otherwise, a meet including a 4-extensor (tetrahedron) and another entity would lead to a 5-bracket.