By R. J. Ellwood, D. Schütz, Annika Raatz, J. Hesselbach (auth.), Jadran Lenarcic, Michael M. Stanisic (eds.)
The publication offers approximately 50 contributions within the zone of robotic kinematics, the fundamental learn sub-field of robotics. the most impetus is at the contemporary advances within the box. This most modern quantity of Advances in robotic Kinematics reviews the most recent medical and applicative effects. All contributions were peer reviewed.
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Extra info for Advances in Robot Kinematics: Motion in Man and Machine: Motion in Man and Machine
Alternately, using the formulation derived in , the following characteristic polynomial is obtained: sin(θ ) = 4408320Y 4 − 1744896Y 3 + 7788032Y 2 − 1464320Y + 3564544 = 0 (11) where 2Y 1 − Y2 and cos(ψ) = , 1 + Y2 1 + Y2 ψ being the angle between the lines defined by P1 P4 and P1 P2 . 9435i. Again, since none of them is real, it can be erroneously concluded that the platform under study cannot be assembled with the given leg lengths thus confirming the results obtained using the formulation proposed in .
1) from Eqs. (2) and (3), hence obtaining: Rx + Sy + Q = 0 (4) Ux + Vy + W = 0 (5) where R = 2b cos(ϕ ) − 2c2 , Q U = 2a cos(ϕ + β ) − 2c3, W S = 2b sin(ϕ ) = ρ12 + ρ22 + c22 + b2 − 2bc2 cos(ϕ ) V = 2a sin(ϕ + β ) − 2d3 = ρ12 + ρ32 + c23 + d32 + a2 − 2a[c3 cos(ϕ + β ) + d3 sin(ϕ + β )] Using Cramer’s rule, x and y can be solved when the determinant ∆ = RV − SU is different from zero. The conditions under which this determinant ∆ vanishes are studied in detail in [10, 13]. A new class of an analytic manipulator was found in  by studying these aforementioned conditions, this type of analytic manipulator possessing the cuspidality phenomenon.
In , the authors obtained analytically the conditions for the existence of cusp points in the joint space for the RPR-2PRR planar parallel manipulator. In this paper, the locus of cusp points for the general 3-RPR planar parallel manipulator will be obtained in a numeric way in the 3-dimensional joint space basing on the conditions developed in . This way, it will be feasible to plan non-singular trajectories between assembly modes by varying the three input variables. Besides, it will be shown that not any path encircling a cusp point enables non-singular assembly mode change but that additional information about the singular curves which are crossed along the path is required.
Advances in Robot Kinematics: Motion in Man and Machine: Motion in Man and Machine by R. J. Ellwood, D. Schütz, Annika Raatz, J. Hesselbach (auth.), Jadran Lenarcic, Michael M. Stanisic (eds.)