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.
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Notes
- 1.
- 2.
It may be noted here is that the last remaining variable, \(\phi _3\), is retained in its trigonometric form while \(\phi _2\) alone is converted to \(t_2\). This helps in further symbolic computations required in the derivation of the FKU (see [5] for the details).
- 3.
The manipulator is singular when \(h_2\) becomes linear in \(t_2\), a case which is not discussed in this paper.
- 4.
All angles are in radians, and lengths in meters, unless mentioned otherwise explicitly.
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Nag, A., Mohan, S., Bandyopadhyay, S. (2017). Forward Kinematic Analysis of the \(3\)-RPRS Parallel Manipulator. In: Wenger, P., Flores, P. (eds) New Trends in Mechanism and Machine Science. Mechanisms and Machine Science, vol 43. Springer, Cham. https://doi.org/10.1007/978-3-319-44156-6_11
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DOI: https://doi.org/10.1007/978-3-319-44156-6_11
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