0
Technical Briefs

# Forward Displacement Analysis and Singularity Analysis of a Special 2-DOF 5R Spherical Parallel Manipulator

[+] Author and Article Information
Xianwen Kong

Department of Mechanical Engineering, School of Engineering and Physical Sciences, Heriot-Watt University, Edinburgh, EH14 4AS, UKx.kong@hw.ac.uk

As pointed out by one of the reviewers of this paper, Eq. 5 can be derived in a more compact manner using one equation in matrix form (22-24).

Please note that if the special 5R SPM is used to orient the axis of R joint 5 (3,5), Type-I singularities of leg 1 occur if the axes of joints 1 and 5 are collinear.

It is noted that it has been identified independently in Ref. 27 and the original version (Kong, X., 2009, “Forward displacement analysis and singularity analysis of a 2-DOF 5R spherical parallel manipulator,” Proceedings of the ASME 2009 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference, Paper DETC2009–87654, August 30–September 2, 2009, San Diego, CA) of this paper that the special 5R SPM always undergoes self-motion in a type-II singular configuration. In Ref. 27, the velocity-equation based approach (26) is used for the singularity analysis.

Architecturally singular parallel manipulators (28-29) are excluded from this paper since they are rarely in use.

J. Mechanisms Robotics 3(2), 024501 (Mar 10, 2011) (6 pages) doi:10.1115/1.4003445 History: Received September 20, 2009; Revised January 08, 2011; Published March 10, 2011; Online March 10, 2011

## Abstract

This paper deals with the forward displacement analysis and singularity analysis of a special 2-DOF 5R spherical parallel manipulator, in which the angle between the axes of any two adjacent revolute joints is a right angle. An alternative formulation of the kinematic equations of the 5R spherical parallel manipulator is proposed. A formula is then derived to produce directly the unique current solution to the forward displacement analysis of the 5R spherical parallel manipulator. It will also be addressed to keep the spherical parallel manipulator in the same working mode and assembly mode by simply restraining the range of an input angle. Unlike other parallel manipulators, the 5R spherical parallel manipulator always undergoes self-motion in a type-II singular configuration, and the 3R leg of the 5R spherical parallel manipulator also always undergoes self-motion in a type-I singular configuration.

<>

## Figures

Figure 1

A 5R spherical parallel manipulator (at the reference configuration)

Figure 2

A 5R spherical parallel manipulator (at type-I singular configuration)

Figure 3

A 5R spherical parallel manipulator (at type-II singular configuration)

Figure 4

A 5R spherical parallel manipulator (at both type-I and type-II singular configurations)

Figure 5

5R spherical parallel manipulator (θ1=π/6, θ2=π/6, and ϕ1=−0.5880 rad)

## Errata

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