Calculation of the Collision-free Printing Workspace for Fully-constrained Cable-Driven Parallel Robots

Using fully-constrained cable robots as manipulators for 3D-printing, there is the risk of collisions between the cables and the printing part. This paper presents a method to calculate the shape of the workspace volume within which a part can be printed without such collisions. The presented method is based on the fact that the printing part is produced in a sequence of horizontal layers. The areas occupied by the cables in the layers are scaled simi­lar mappings of the cross-sections of the printing part. There is no collision if the 2D-shapes occupied by the cables in the print­ing layer do not overlap with the cross-sections of the printing part in the same layer. A procedure to find the largest printable 2D-shapes within the class of parallelograms for each layer is developed. The maximum printable 3D-volume is then given by stacking the 2D-shapes of each layer. Figures show the results of the method applied on the cable robot IPAnema 3. Finally, a guideline for the design of fully-constrained cable robots to max­imize their printable volume is given.