Abstract
A dimensional synthesis of parallel manipulators (PMs) consists of determining the values of the geometric parameters that affect the platform motion so that a useful workspace with assigned sizes can be suitably located in a free-from-singularity region of its operational space. The main goal of this preliminary dimensioning is to keep the PM far enough from singularities to avoid high internal loads in the links and guarantee a good positioning precision (i.e., for getting good kinematic performances). This paper presents a novel method for the dimensional synthesis of translational PMs (TPMs) and applies it to a TPM previously proposed by the author. The proposed method, which is based on Jacobians’ properties, exploits the fact that TPM parallel Jacobians are block diagonal matrices to overcome typical drawbacks of indices based on Jacobian properties. The proposed method can be also applied to all the lower-mobility PMs with block diagonal Jacobians that separate platform rotations from platform translations (e.g., parallel wrists).
Highlights
Designing the mechanical structure of a general-purpose machine, like a manipulator, has three mandatory steps that transform the original intuition of the designer into a real device: type synthesis [1,2,3,4], dimensional synthesis [1,2,4], and machine-element design [5,6,7]
translational PMs (TPMs) of the 3-URU type [35] feature three equal limbs constituted of two links, one adjacent to the base and the other to the platform, joined to one another through a revolute (R)-pair and to the platform or to the base through a universal (U)-joint, that is, they are of the URU type
The dimensional synthesis of the Laboratory of Mechatronics and Virtual Prototyping (LaMaViP) 3-URU clearly proves that the novel method proposed for evaluating TPMs’ kinetostatic performances is based on three indices whose meaning is easy to understand during the design of the machine
Summary
Designing the mechanical structure of a general-purpose machine, like a manipulator, has three mandatory steps that transform the original intuition of the designer into a real device: type synthesis [1,2,3,4], dimensional synthesis [1,2,4], and machine-element design [5,6,7]. In the parallel-manipulator (PM) design, the dimensional synthesis [8,9,10] consists of determining the values of the above-mentioned geometric parameters (i.e., in this case, the ones that affect the platform motion) so that a useful workspace with assigned sizes can be located in a region of the operational space that is far from singularities. Satisfying this condition makes it possible to avoid high internal loads in the links and to guarantee a good positioning precision (i.e., to get good kinematic performances). This type of preliminary dimensioning is usually addressed [10,11,12,13] by using condition number [14,15,16] or manipulability [17] or transmission indices [18,19,20,21] as objective functions to optimize
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