Novel Kinematically Redundant (3+1)-DOF Delta-Type Parallel Mechanisms

Although parallel mechanisms are used in various fields, their application is often limited by singularities and a restricted workspace. Kinematic redundancy is a promising approach for mitigating these issues while also extending the functionality of the mechanisms. This article contributes to this field by introducing two novel Delta-type kinematically redundant parallel mechanisms with linear actuators. The moving platform in these mechanisms has three translational degrees of freedom and consists of two parts connected by a prismatic joint, providing an extra translation between the parts. First, we present closed-form solutions to the inverse and forward kinematic problems, accompanied by numerical examples that validate the theoretical derivations. Next, we analyze singular configurations of the mechanisms with a symmetrical design, focusing on parallel singularities. Using an iterative approach, we identify points within the workspace corresponding to these configurations, including finite-motion singularities. Based on this analysis, we changed the geometrical parameters of one mechanism and presented the design where the singularity-free region of the workspace occupies 95% of the total workspace. This study forms the basis for future research on the proposed mechanisms and their prototyping.