Maximal singularity-free distribution of input parameters in a parallel manipulator considering load deformations and clearances

It is well known that singularities are inherent to parallel manipulators and have serious influence on their properties. It is desired that the motion uncertainty caused by the singularity should be avoided in the design and operation stages. The singularity distribution hypersurface shows the relations among the pose components at the singular points, but it is difficult to be utilized in predicting the motion certainty through checking and controlling the lengths of input parameters. In this article, taking a 3-RPR parallel manipulator as an example, and considering the clearances existing in the joints and the deformations of the input actuating cylinders under external loads, the maximal singularity-free distribution of input parameters is investigated. While the input parameters are located within the space enveloped by the maximal singularity-free distribution surfaces, the manipulator can bear the required external loads and give out a certain motion at the neighbourhood of singular points. Based on this kind of the maximal singularity-free distribution of input parameters, the singularity can be avoided both in the early design stage by assigning the input parameters into a suitable region and in the operation state through controlling and monitoring the values of the input parameters.