Investigation of Interference-Free Workspace of a Cartesian (3-PRRR) Parallel Manipulator

Numerical investigations, development and control of a cartesian (3-PRRR) parallel manipulator

“…This section analyses the effect of various end-effector shapes on the interference-free workspace of the 3-dof CPM. The kinematic modelling 29 and the interference-free workspace estimation 25 of the CPM were already analysed in previous works. By incorporating the changes because of the different shapes in the kinematic model, 29 the interference-free workspace of all the cases is determined.…”

“…The kinematic modelling 29 and link interference-free workspace analyses 25 the remaining variants 2, 3 and 4 are compared against the benchmark, while maintaining the corresponding link lengths the same as that of the benchmark. The effect of offset distance of the actuator axis on the interference-free workspace is also analysed in the following sections.…”

“…The interference algorithm 25 predicts four independent regions of link interference for the benchmark variant Figure 3(a) which are, respectively, the intra-limb collision in limbs 1,2 and 3 and the inter-limb interference between leg 3 and the moving platform. Four random end-effector coordinates from each of these regions are selected and the predicted interference is validated using a CAD package called Onshape, as shown in Figure 6.…”

“…As a rule of thumb, the minimal Z axis limit should be kept above the collision-threshold value. 25 For the example shown in Figure 2, the minimal limits are as follows: X min = p 4 ; Y min = p 1 . With reference from Figure 2, the maximum limits of the XYZ workspace are defined as follows: X max = min ([( k 3 + e 3 + f 3 + p 4 ); ( e 2 + f 2 )]); Y max = min ([( e 1 + f 1 + p 1 ); ( e 3 + f 3 )]); Z max = min ([( k 1 + e 1 + f 1 ); ( k 2 + e 2 + f 2 )]); A similar procedure is adopted for the various configurations of interest and the resulting rectangular-prism labelled as XYZ , is supplied to step 1 of Algorithm 1.…”

“…The consequence of such irregularities is that the variance in workspace ranges in three coordinate axes can be quite high, which essentially limits the workspace of the mechanism in one or more directions. The algorithms developed in our previous work 25 provides a solution to this issue by filtering out a regular-shaped square-cuboid of maximal volume that inscribers the interference-free workspace.…”