0
Technical Briefs

# A $3-ṞPR$ Parallel Mechanism With Singularities That are Self-Motions

[+] Author and Article Information
Novona Rakotomanga

Department of Automated Manufacturing Engineering, École de technologie supérieure (ÉTS), Montreal, QC, H3C 1K3 Canada

Ilian A. Bonev

Department of Automated Manufacturing Engineering, École de technologie supérieure (ÉTS), Montreal, QC, H3C 1K3 Canadailian.bonev@etsmtl.ca

It is customary to refer to parallel mechanisms using the symbols $P$ and $R$, which stand for prismatic and revolute joints, respectively. When a joint is actuated, its symbol is underlined.

J. Mechanisms Robotics 2(3), 034502 (Jul 14, 2010) (4 pages) doi:10.1115/1.4001737 History: Received May 04, 2009; Revised January 07, 2010; Published July 14, 2010; Online July 14, 2010

## Abstract

The Cartesian workspace of most three-degree-of-freedom parallel mechanisms is divided by Type 2 (also called parallel) singularity surfaces into several regions. Accessing more than one such region requires crossing a Type 2 singularity, which is risky and calls for sophisticated control strategies. Some mechanisms can still cross these Type 2 singularity surfaces through “holes” that represent Type 1 (also called serial) singularities only. However, what is even more desirable is if these Type 2 singularity surfaces were curves instead. Indeed, there exists at least one such parallel mechanism (the agile eye) and all of its singularities are self-motions. This paper presents another parallel mechanism, a planar one, whose singularities are self-motions. The singularities of this novel mechanism are studied in detail. While the Type 2 singularities in the Cartesian space still constitute a surface, they degenerate into lines in the active-joint space, which is the main result of this paper.

<>

## Figures

Figure 1

General 3-ṞPR planar parallel mechanism

Figure 2

The new 3-ṞPR planar parallel mechanism and its two assembly modes

Figure 3

Reciprocal screws and Type 2 singularities: (a) a nonsingular configuration and (b) a Type 2 singular configuration

Figure 4

Type 2 singularity loci (the solid-line circle) for a given orientation

Figure 5

Cardanic self-motion of the mobile platform present in any Type 2 singular configuration

Figure 6

Type 2 singularity loci form the same circle for any orientation

Figure 7

Type 2 singularity loci in the active-joint space of a general 3-ṞPR planar parallel mechanism

Figure 8

Type 1 and Type 2 singularity loci in the active-joint space for the mechanism studied

Figure 9

For a given orientation, three points from the Type 2 singularity circle correspond to Type 1 singularities

Figure 10

Proposed mechanical design of the mechanism under study

## Discussions

Some tools below are only available to our subscribers or users with an online account.

### Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related Proceedings Articles
Related eBook Content
Topic Collections