In study this paper, a geometric formulation is proposed to describe the workspace of parallel manipulators by using a recursive approach as an extension of volume generation for solids of revolution. In this approach, the workspace volume and boundary for each limb of the parallel manipulator is obtained with an algebraic formulation derived from the kinematic chain of the limb and the motion constraints on its joints. Then, the overall workspace of the mechanism can be determined as the intersection of the limb workspaces. The workspace of different kinematic chains is discussed and classified according to its external shape. An algebraic formulation for the inclusion of obstacles in the computation is also proposed. Both analytical models and numerical simulations are reported with their advantages and limitations. An example on a 3-SPR parallel mechanism illustrates the feasibility of the formulation and its efficiency.

Russo, M., Ceccarelli, M. (2022). A geometrical formulation for the workspace of parallel manipulators. ROBOTICA, 40(8), 2581-2591 [10.1017/S0263574721001806].

### A geometrical formulation for the workspace of parallel manipulators

#### Abstract

In study this paper, a geometric formulation is proposed to describe the workspace of parallel manipulators by using a recursive approach as an extension of volume generation for solids of revolution. In this approach, the workspace volume and boundary for each limb of the parallel manipulator is obtained with an algebraic formulation derived from the kinematic chain of the limb and the motion constraints on its joints. Then, the overall workspace of the mechanism can be determined as the intersection of the limb workspaces. The workspace of different kinematic chains is discussed and classified according to its external shape. An algebraic formulation for the inclusion of obstacles in the computation is also proposed. Both analytical models and numerical simulations are reported with their advantages and limitations. An example on a 3-SPR parallel mechanism illustrates the feasibility of the formulation and its efficiency.
##### Scheda breve Scheda completa Scheda completa (DC)
2022
Pubblicato
Rilevanza internazionale
Articolo
Esperti anonimi
Settore ING-IND/13 - MECCANICA APPLICATA ALLE MACCHINE
English
workspace
parallel manipulators
kinematics
algebraic workspace
geometric workspace
Russo, M., Ceccarelli, M. (2022). A geometrical formulation for the workspace of parallel manipulators. ROBOTICA, 40(8), 2581-2591 [10.1017/S0263574721001806].
Russo, M; Ceccarelli, M
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Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/2108/313756`
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