Download Advances in Robot Kinematics: Motion in Man and Machine: by R. J. Ellwood, D. Schütz, Annika Raatz, J. Hesselbach PDF

By R. J. Ellwood, D. Schütz, Annika Raatz, J. Hesselbach (auth.), Jadran Lenarcic, Michael M. Stanisic (eds.)

The e-book presents approximately 50 contributions within the sector of robotic kinematics, the elemental learn sub-field of robotics. the most impetus is at the contemporary advances within the box. This most recent quantity of Advances in robotic Kinematics reviews the latest clinical and applicative effects. All contributions were peer reviewed.

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Extra resources for Advances in Robot Kinematics: Motion in Man and Machine: Motion in Man and Machine

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Acknowledgements We are very much indebted to Philippe Wenger and his colleagues from IRCCyN who inspired this work. We also gratefully acknowledge the financial support of the 32 N. Rojas and F. Thomas Autonomous Government of Catalonia through the VALTEC programme, cofinanced with FEDER funds, and the Colombian Ministry of Communications and Colfuturo through the ICT National Plan of Colombia. References 1. : Parallel Robots, Kluwer Academic Publishers, Dordrecht, (2000). 2. : Solution polynomiale au probl`eme de la cin´ematique directe des manipulateurs parall`eles plans a` 3 degr´es de libert´e.

As a result, a 6th-degree characteristic polynomial, which is not linked to any particular reference frame, is obtained in a straightforward manner without variable eliminations nor tangent-half-angle substitutions. Moreover, the obtained polynomial is mathematically more tractable than the one obtained using other approaches because its coefficients are the result of operating with Cayley– Menger determinants with geometric meaning. This paper is organized as follows. A coordinate-free formula for bilateration expressed in terms of Cayley–Menger determinants is presented in Section 2.

48 M. Ur´ızar et al. (a) (b) Fig. 2 (a) DKP singularity locus in the joint space. (b) Joint space section for ρ1 = 2. 3 Locus of Cusp Points The conditions for obtaining the cusp points in the joint space have been developed in [12]. These latter conditions are the following: g = 0, h= ∂g = 0, ∂ϕ ∂h ∂ 2g = =0 ∂ϕ ∂ ϕ2 (7) The first condition, g = 0, establishes that cusp points belong to the workspace, that is, they are DKP solutions of the manipulator and thus, they verify the expression of the characteristic polynomial.

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