DYNA JOURNAL ENGINEERING

Key words:

Continuum parallel manipulator; Deformable elements; Cosserat Model; Kirchhoff Model; Kinematics; Stability analysis; Flexible Delta robot; Lower-mobility mechanisms; Parasitic motions; Tripod manipulators.

Article type:

ARTICULO DE INVESTIGACION / RESEARCH ARTICLE

Section:

RESEARCH ARTICLES

Continuum Parallel Manipulators are parallel kinematic mechanisms in which rigid elements have been replaced by very flexible slender rods, eliminating some kinematic joints and maintaining closed-loop kinematic chains. The mobility of the resulting mechanism is due to the combination of kinematic joints and deformability of the slender bars. Its advantages over rigid element mechanisms can be summarized as follows: simpler assembly, lower weight, larger workspace for the same dimensions and lower stiffness. The latter feature implies a lower risk in the case of impacts when the mechanism is designed for collaborative tasks in a non-isolated space where robots and people meet simultaneously, thus possessing a high potential in the field of so-called CoBots. This same characteristic makes it necessary to consider in the design two aspects that do not appear in rigid mechanisms.

The main objective of this paper is to explain the basic methodology to be followed when analyzing continuum parallel mechanisms, both planar and spatial, with emphasis on problems that arise due to the incorporation of flexible elements, such as the non-stability of certain solutions and the existence of parasitic movements in spatial mechanisms of low mobility. In the first part, it will be shown how the resolution of position kinematic problems requires that not only geometrical constraint equations are taken into account, but also others that guarantee the equilibrium of forces and moments, also considering the non-linearity of the large deformations of the bars. In general, the problem presents a multiplicity of kinetostatic solutions. In this work, the multiplicity of solutions for the case of planar flexible mechanisms will be addressed, in addition to their stability analysis.

In the case of lower-mobility spatial mechanisms, it must be taken into account that these flexible systems are in essence systems with infinite degrees of freedom, so that a complete restriction of motions is not possible. Consequently, in the operation of this subclass of mechanisms, the so-called parasitic motions will appear, inherent to the flexibility of the members, which complicate the kinematic analysis. The present paper analyzes this type of parasitic motions, which until now had only been investigated in rigid manipulators, and shows their evolution in the manipulator workspace. The theoretical analysis of these motions has been contrasted with experimental tests based on the prototype of the flexible Delta manipulator.