Kinematic and Dynamic Analysis of Spatial Six Degree of Freedom ...

Figure 1.4 - The first flight simulator based on an octahedral hexapod (courtesy of Klaus Cappel)
In general, parallel manipulators provide superior precision, robustness, stiffness and
load capacity in excess of workspace, in contrast to conventional serial manipulators. In
various tasks, parallel manipulators are used as vehicle simulators, high-precision machine
tools, torque/force sensors, industrial robots and alike. They are also used for
laser/camera/antenna positioning, ophthalmic surgery, et cetera. With the accumulation of the
knowledge in this area, the areas of application for the parallel manipulators are growing
rapidly. In a sense, walking machines with many legs are parallel manipulators such that, the
feet touching the ground can be idealized as spherical joints and the body as the moving
platform.
The most common type of parallel structure is the six degree of freedom (DOF)
Stewart-Gough Platform. Many researchers proposed different designs, along with many
different techniques and methods to solve the problems of kinematics [2-9], dynamics [10-15]
control [16-21], design [22] and optimization [23-26].
As indicated, much research has been done on the problem of forward kinematics. In
contrast to serial manipulators, forward kinematics of a parallel manipulator is very hard to
solve. Although closed form/analytical solutions are obtained for simpler parallel
manipulators [27], numerical techniques are generally being used for their spatial
counterparts. This complexity is due to the highly non-linear nature of equations governing
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