Abstract
The identification of singularities is an important aspect of research in parallel manipulators, which has received a great deal of attention in the past few decades. Yet, even in many well-studied manipulators, very few reported results are of complete or analytical nature. This chapter tries to address this issue from a slightly different perspective than the standard method of Jacobian analysis. Using the condition for existence of repeated roots of the univariate equation representing the forward kinematic problem of the manipulator, it shows that it is possible to gain some more analytical insight into such problems. The proposed notions are illustrated by means of applications to a spatial \(3\)-RPS manipulator, leading to the closed-form expressions for the singularity manifold of the \(3\)-RPS in the actuator space.
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Notes
- 1.
If constraint equations are written in, or, converted to, their algebraic (i.e., polynomial) forms, then an equivalent condition for such singularities would be that the singularity condition in Eq. (2) in its algebraic form, belongs to the constraint ideal generated by the algebraic form of Eq. (1). Thus, the determination of singularities in the constraint equations can also be posed as an ideal membership (see, e.g., [4]) problem.
- 2.
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Srivatsan, R.A., Bandyopadhyay, S. (2014). Analysis of Constraint Equations and Their Singularities. In: Lenarčič, J., Khatib, O. (eds) Advances in Robot Kinematics. Springer, Cham. https://doi.org/10.1007/978-3-319-06698-1_44
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DOI: https://doi.org/10.1007/978-3-319-06698-1_44
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