Abstract
This paper presents a comprehensive study of the forward kinematic problem of a newly introduced spatial parallel manipulator, namely, the 3-RPRS manipulator. The manipulator has three legs with two actuators in each, which connect a moving triangular platform to a fixed base. Three loop-closure equations are formed with the three passive joint angles in the legs, as the unknowns, which 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 variables. Furthermore, it is found that the polynomial has only the even-powered terms, leading to 8 pairs of solutions. One solution in each pair represents a pose on one side of the fixed base, and the other, a reflection of the same at the said base plane. The theoretical developments are illustrated via several numerical examples, one of which yields 16 real solutions, thus establishing that the obtained univariate polynomial is minimal in its degree. The results obtained are validated numerically, as well as verified against the inverse kinematics of the manipulator, 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.
