Abstract
This paper presents a comprehensive analytical solution to the forward kinematic problem of a newly introduced spatial parallel manipulator, namely, the \(3\)-RPRS. The manipulator has three legs with two actuators in each, which connect a moving triangular platform to a fixed base. Loop-closure equations are formed to find the unknown passive rotary joint angle in each leg. These equations are subsequently reduced to a single univariate polynomial equation of degree 16. The coefficients of this equation are obtained as closed-form functions of the architecture parameters of the manipulator and the input joint angles, and therefore the analysis covers all possible architectures and configurations. Furthermore, it is found that the polynomial has only the even powers, therefore leading to 8 pairs of solutions, each pair being mirrored at the base platform. The theoretical developments are illustrated via a numerical example. The results obtained are validated by checking the residues of the original loop-closure equations, thereby establishing the correctness of the formulation as well as the results.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
