# Stewart Platforms

A Stewart Platform based Flight Simulator for F-16 (Source: NLR Netherlands)

``` A Puma robot mounted on a Stewart Platform
(Source: Robotic Manipulation/ Murray, Li, Shastri)```
A Stewart Platform basically consists of a base (lower platform) and end effector (top platform) connected by six actuator driven legs. In order to change the position of the top platform relative to the bottom platform all the six legs move in a coordinated direction and produce the desired displacement.

The Stewart platforms can be classified into different configurations. The most general Stewart platform is the 6-6 platform, where the legs connect to six different points on the base and six different point on the top platform. The general configuration is given by "B-P", where B is the number of points legs connect to the base and P is the number of points legs connect to the top platform. Thus, the configuration for the two Stewart Platforms shown above would be 3-3.

The Configuration may also be given as "6-p", where p is the number of points legs join the upper platform. Thus, the two platforms shown in the figure above would have configuration of 6-3.

The issue of kinematics is a major issue in Stewart Platforms. Its inverse kinematics, like any parallel manipulator, is easy to figure out. But, its Direct Kinematics, or Forward Displacement Analysis (FDA) is very tough. In fact, the FDA for the most general Stewart Platform i.e 6-6 has not been solved yet.

It has been analytically found out that the maximum number of solutions for most general Stewart Platform would theoretically be 40. This is an extremely non-linear equation and shows why the FDA might be difficult.

As the platform is constrained, the number of solutions decrease. For less general cases the Direct kinematics has been successfully solved. It is now widely acknowledged that the maximum number of solutions for most cases is 16.

For machine tool applications the issue of stiffness plays a major role in selecting th econfiguration. As the Octahedral Structure is supposed to be the most rigid structure, the structures resembling that should be chosen. Since 6-3 is an octahedral structure it is chosen for most machine tool applications.

Applications issue also require accurate solution of trajectory path verification and workspace calculations