## 2 Related Work
[PERSON] et al. [12] built the virtual prototype for a 3-UPS/S parallel mechanism in ADAMS. It was used as an assistive exoskeleton for a human hip joint. It performed human hip movements (flexion/extension, adduction/abduction, and external/internal rotation). The forward kinematic analysis was solved and verified by building a parametric model in MATLAB. [PERSON] et al. [13] designed and fabricated a prototype of 3-UPS/S robot as a parallel airborne stabilized platform. Their research findings made it possible to conclude that for successive forward kinematic analysis, the Finite-Step-Integration method has good arithmetic accuracy and speed. Using this method, it was demonstrated that the aerial stabilized platform workspace is sufficient and the method was also quick and accurate in motion tracking. [PERSON] et al. (2014) designed a 3 UPS1S for laparoscopic applications. The prototype was designed to cover the necessary workspace needed for this type of surgical technique. The device permits the positioning of a MIRS (Robotized Minimal Invasive Surgery) surgical instrument. Screw theory was used for kinematic analysis. [PERSON] et al. (2015) used a 3-UPS/RPU architecture for knee diagnosis and rehabilitation. Applying the inverse kinematic model, the leg motion of the robot was studied, and then using the leg motion through the simulation of the workspace of the robot, it was shown that the robot end-effector was able to follow a prescribed task. [PERSON] et al. (2016) used 3-UPS/S as a shipborne stable platform to compensate ship orientation fluctuation and isolated the influence of wind and waves on shipborne equipment. Hence, an efficient and accurate control strategy was developed for this purpose in their study. [PERSON] et al. (2017) proposed a 3-PUS/S SPM with three rotational motions. Furthermore, the application-specific study of its kinematic equations, singularity, and design optimization was conducted. The three legs of the proposed parallel robot, each with three prismatic joints, allow for an infinite rotation around the Z-axis. Because of this, the robot has huge workspace and good versatility. Using the Jacobian matrix, the singularity of the robot was found. Then, the optimum dimensions of the manipulator were studied by the Genetic Algorithm (GA), and the Global Condition Index (GCI) was maximized. When encountering parallel singularities, PMs may sustain significant damage because the actuator forces needed to maintain the platform's trajectory may approach infinity. It is crucial to determine whether a singularity-free path may lead to a desirable pose of the platform in the workspace and, if so, which path should be taken in the first instance. It is therefore very important to avoid singularity in PMs (2018). A numerical method developed by [PERSON] (2018) was able to find a path connecting any two points in the workspace that is devoid of singularities. This method can be applied to all 3 UPS and 3 UPU manipulators which do not possess degenerate non-singular critical points of the Jacobian determinant. [PERSON] (2019) determined the assembly modes of the 3 UPS-S manipulator by modelling the forward displacement analysis using [PERSON] formula. By choosing one of the assembly modes as a home posture, the suggested strategy made it simple to prevent singularity configuration. [PERSON] et al. (2020) demonstrated that, with regard to singularity, the velocity analysis and mechanical analysis were consistent for the 3 UPS/S parallel machine. They also demonstrated that, as the manipulator approaches singularity, the accuracy and actuator force attributes declined. [PERSON] et al. (2021) showed that the Tilt-and-Torsion angles were a powerful geometric tool for the analysis of Type 2 singularities in 3-UPS/S manipulators. They also derived the workspace boundaries (Type 1 singularity loci) using this method (2022). The geometric relationship between the singular configuration of the 3 UPS-S parallel mechanism and its single kinematic screw was explained and made clearer in a study by [PERSON] et al.