# Determination of 6D workspaces of Gough-type parallel manipulator and comparison between different geometries

## Abstract

The author considers in this paper a Gough-type parallel robot whose leg length values are constrained to lie within some fixed ranges and for which there may be mechanical limits for the motion of the passive joints. The purpose of this paper is to present algorithms to determine: the constant orientation workspace; all the possible locations of the center of the platform that can be reached with a fixed orientation; the total orientation workspace: all the possible locations of the center of the platform that can be reached with any orientation in a set defined by three ranges for the orientation angles; the inclusive orientation workspace: all the possible locations of the center of the platform that can be reached with at least one orientation among a set defined by three ranges for the orientation angles. Most of these algorithms are based on a basic methods: approximation of the results by a set of 3D or 6D boxes obtained from an initial estimation through a bisection process. The boxes in the result will either fully or partially lie inside the workspace: the bisection stops as soon as all the boxes that do not lie fully inside the workspace have amore »

- Authors:

- Publication Date:

- Research Org.:
- INRIA Sophia-Antipolis (FR)

- OSTI Identifier:
- 20001200

- Resource Type:
- Journal Article

- Journal Name:
- International Journal of Robotics Research

- Additional Journal Information:
- Journal Volume: 18; Journal Issue: 9; Other Information: PBD: Sep 1999; Journal ID: ISSN 0278-3649

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATION; ROBOTS; MANIPULATORS; CALCULATION METHODS; CONTROL THEORY; CONTROL SYSTEMS

### Citation Formats

```
Merlet, J.P.
```*Determination of 6D workspaces of Gough-type parallel manipulator and comparison between different geometries*. United States: N. p., 1999.
Web. doi:10.1177/02783649922066646.

```
Merlet, J.P.
```*Determination of 6D workspaces of Gough-type parallel manipulator and comparison between different geometries*. United States. doi:10.1177/02783649922066646.

```
Merlet, J.P. Wed .
"Determination of 6D workspaces of Gough-type parallel manipulator and comparison between different geometries". United States. doi:10.1177/02783649922066646.
```

```
@article{osti_20001200,
```

title = {Determination of 6D workspaces of Gough-type parallel manipulator and comparison between different geometries},

author = {Merlet, J.P.},

abstractNote = {The author considers in this paper a Gough-type parallel robot whose leg length values are constrained to lie within some fixed ranges and for which there may be mechanical limits for the motion of the passive joints. The purpose of this paper is to present algorithms to determine: the constant orientation workspace; all the possible locations of the center of the platform that can be reached with a fixed orientation; the total orientation workspace: all the possible locations of the center of the platform that can be reached with any orientation in a set defined by three ranges for the orientation angles; the inclusive orientation workspace: all the possible locations of the center of the platform that can be reached with at least one orientation among a set defined by three ranges for the orientation angles. Most of these algorithms are based on a basic methods: approximation of the results by a set of 3D or 6D boxes obtained from an initial estimation through a bisection process. The boxes in the result will either fully or partially lie inside the workspace: the bisection stops as soon as all the boxes that do not lie fully inside the workspace have a size that is lower than a fixed threshold. The paper includes a comparison between the workspace volumes of four different robot geometries, which shows that for robots of similar dimensions the joints layout has a large influence on the workspace volume.},

doi = {10.1177/02783649922066646},

journal = {International Journal of Robotics Research},

issn = {0278-3649},

number = 9,

volume = 18,

place = {United States},

year = {1999},

month = {9}

}