Design of Linear Delta Robot: Compromise Between Manipulability and Workspace Size
An optimal kinematic design method suited for parallel manipulators is developed. The kinematic optimization process yields a design, which delivers the best compromise between manipulability and a new performance index, space utilization. It is shown tha
- PDF / 1,264,835 Bytes
- 10 Pages / 481.89 x 691.654 pts Page_size
- 72 Downloads / 179 Views
Abstract. An optimal kinematic design method suited for parallel manipulators is developed. The kinematic optimization process yields a design, which delivers the best compromise between manipulability and a new performance index, space utilization. It is shown that the exhaustive search minimization algorithm is effective for as many as four independent design variables and presents a viable alternative to advanced non-linear programming methods. The manipulability generally exhibits relatively little variation when compared to space utilization. The tendency exists for the solution to converge on a zero workspace size architecture when manipulability is optimized alone. The inclusion of the space utilization index in the cost function is crucial for obtaining realistic design candidates.
1
Introduction
The literature contains much information regarding the history and various types of parallel robots, e.g. (Merlet, 1990). Most important here, however, is the development of the DELTA by Clave! at EPFL in Lausanne (Clave!, 1991, Miller and Clave!, 1992 ). The Linear Delta, Figure 1, is an adaptation of the DELTA, which results from replacing the revolute actuators and upper arms with three parallel linear actuators or rails. Whilst there exist several methods of determining the volume and boundaries of parallel manipulators' workspaces (Carretero et al., 1998, Stamper eta!., 1997, Wang and Hsieh, 1998), the simplicity of the Linear Delta's geometry allows a relatively simple analysis to be carried out and analytical solutions obtained. This phenomena is exploited to greatly simplify the process of kinematic optimization. The kinematic optimization is carried out with the goal of reaching a compromise between two often-conflicting design goals: manipulability and workspace size. Maximization of the workspace volume alone tends to produce parallel manipulator being singular in all configurations, whilst considering manipulability in isolation may lead to architectures with relatively small workspaces; a clear example of this phenomena may be found in the results of (Stamper et al., 1997). Accordingly, the objective function considered here is a weighted sum oftwo performance indices. The first index is based on that of(Gosselin and Angeles, 1989), and measures the inverse of the Jacobian's condition number. In order to overcome the limitations associated with the use of
1
Presently at Advanced Analysis Group- Worley Engineering, Perth, Australia. corresponding author, [email protected]
G. Bianchi et al. (eds.), Romansy 14 © Springer-Verlag Wien 2002
398
M. Stock and K. Miller
this index in isolation, a new performance index is proposed, which measures space utilization, and reflects the ratio of the workspace size to the physical size of the robot's structure.
Travelling Plate (End Effector)
Figure I. Render MATLAB representation of the Linear Delta.
2
Workspace Cross-Section Analysis for Linear Delta
The structural parameters of the Linear Delta, as shown in Figures 2 and 3, may be summarized as
Data Loading...
