By Gang Shen, Yukio Takeda, Hiroaki Funabashi (auth.), J. Lenarčič, F. Thomas (eds.)

This is the 5th publication of the Kluwer's sequence Advances in robotic Kine matics. The publication offers the newest examine advances within the concept, layout, regulate and alertness of robot structures, that are meant for numerous reasons corresponding to manipulation, manufactur ing, 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 structures. tools used comprise line geometry, quaternion algebra, screw alge bra, and linear algebra. those tools are utilized to either parallel and serial multi-degree-of-freedom platforms. the consequences should still curiosity researchers, academics and scholars, in fields of engineering and mathe matics regarding robotic conception, layout, keep watch over and alertness. every one contribution during this publication have been carefully reviewed through or 3 self sufficient reviewers and fifty three articles have been urged for e-book. we're satisfied to monitor that Advances in robotic Kine matics has continuously attracted the main notable authors and has de veloped a outstanding clinical group within the sector. Many very important and unique clinical effects have been for the 1st time pronounced and dis stubborn in those books. All articles during this publication have been additionally stated on the 8 overseas symposium on Advances in robotic Kinematics that used to be organised in June 2002 in Caldes de Malavella in Spain.

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Uk Abstract The geometry of a 3D octahedral parallel robot manipulator system is specified in terms of two rigid octahedral structures (the fixed and moving platforms) and six actuation legs. The symmetry of the system is exploited to determine the behaviour of (a new version of) the quality index for various motions. The main results are presented graphically. Keywords: parallel robot, quality index, rotation symmetry 1. Introduction In recent years there has been much interest in the geometry of the Stewart platform (Stewart, 1965) and this work has led to the development of various parallel manipulation systems.

23) o Finally, adding up Eqs. 22 & 23 yields the relation sought. Example. To verify the validity of the foregoing theorem, assume that for a certain body, its Euler angles (¢, 0, 1jJ) have been taken as the generalized coordinates. We will demonstrate that Eq. 20 holds. To this end, notice that the angular velocity of a rigid body in terms of the Euler angles and their time rates are given by w = [~sin 0 sin 1jJ + 19 cos 1jJ ~ sin 0 cos 1jJ - Setting q £ [¢ 19 sin 1jJ ~ cos 0 + ~ ] T 0 1jJJ T, J w and its time rate can then be found as a [Sin 0 sin 1jJ cos 1jJ cosO 0 Jw == a~ = sin 0 cos 1jJ - sin 1jJ Jw = [ 0 cos 0 cos 1jJ.

The 3D octahedral platform and some axes of rotation symmetry The latter has three 4-fold axes of rotation symmetry (each passing through a pair of opposite vertices), four 3-fold axes of rotation symmetry (each passing through the centers of a pair of opposite faces), and six 2fold axes of rotation symmetry (each passing through the centers of a pair of opposite edges). There are also several types of planes of reflection symmetry, one of which passes through two opposite vertices and bisects the solid octahedron.