It was demonstrated that there exists a class of parallel mechanisms with zero torsion, which are referred to as zero-torsion parallel mechanisms. proposed the advantages of the T&T angles for the study of spatial parallel mechanisms in-depth. With the presence of spherical joints in a parallel mechanism, the modified Euler angles, otherwise known as the “Tilt and Torsion” (T&T) angles, could be employed. Moreover, the inverse kinematics, in general, is easier to solve for parallel robots, especially when prismatic joints are employed. At present, many researchers work on parallel robots as they offer simple and conventional designs with ease of calibration. The performance of parallel robots varies within their workspace, which is considerably smaller when compared to serial robots. PKMs offer better accuracy, lower mass/inertia properties and high structural stiffness. Parallel kinematics machines (PKM) have interesting applications in industries over serial machines. The outcome of this study will be helpful for the integration of the mechanism for a piping inspection robot and also for the analysis of stacked architectures. Experimental validation is then carried out on the prototype of the mechanism to perform a circular trajectory, in line with the simulations. Initially, simulations are performed using the results of singularity analysis to have a comparison between the T&T space and the Euler space. These workspaces can then be mapped to the Euler angles of the universal joint and the relation between the T&T space and the Euler space is demonstrated and validated in this study. The singularity-free workspace and the tilt limits of the mechanism are disclosed through this method.

Thus, the positioning of the mobile platform for the mechanism is analyzed using the theory of Tilt and Torsion (T&T). However, this approach is computationally expensive especially when stacked structures are analyzed. The usual singularity approach is carried out with respect to the Euler angles of the universal joint.

This article presents the analysis of a parallel mechanism of type 3-S PS-U.

Cad mapping