171 TECHNICAL UNIVERSITY OF CLUJ-NAPOCA ACTA TECHNICA NAPOCENSIS Series: Applied Mathematics, Mechanics, and Engineering Vol. 57, Issue II, June, 2014 THE WORKSPACE AND THE SINGULARITIES OF THE 3KTK SPATIAL PARALLEL MANIPULATOR Claudiu Mihai NEDEZKI, Adrian TRIF, Gheorghe KEREKES Abstract: In this article is studied the graphical representation using the meshing method (based on input- output equations and on a program designed in AutoLISP - AutoCAD) for the workspace and for the singularities of the 3KTK manipulator with 3 degrees of freedom in translation. Is calculated the areas of the different plane sections (Zp = constant), and the workspace volume. It shows the influence of the the constructive parameters on the workspace of the manipulator. Key words: parallel manipulator, the meshing method, the Jacobian matrix, the input - output equations, the singularities, degrees of freedom. 1. INTRODUCTION The figure 1 shows the kinematic scheme of the 3KTK spatial parallel manipulator having three degrees of freedom in translation and three identical kinematic chains (KTK - subsequent joints type of kinematic chain from the base to the final element K - cardan, T - translation). Fig. 1 The kinematic scheme of the manipulator Only an arrangement of the kinematic chains in the three joints according to fig. 1 leads to a spatial parallel mechanism with three degrees of freedom in translation [1], [2]. According to some Korean researchers [3], the clearances of the cardan joints must be less than 0,05 0 . 2. THE GRAPHICAL REPRESENTATION FOR THE WORKSPACE OF THE 3KTK MANIPULATOR USING THE MESHING METHOD For the 3KTK parallel manipulator the question arises it will determine the workspace in translation because the manipulator’s platform executes only spatial translations. Obtaining workspace is achieved using the computer [4], [5], [6], [7]. It is starts from analytical solution of the inverse problem of the positions deduced in [1] and [2]. [ ] [ ] 2 2 2 ) ( sin ) ( cos ) ( h Z R r Y R r X q P i P i P i − + − + + − + ± = δ δ (1)