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

3.3 Geometrical Structural Synthesis of Parallel Manipulators
The purpose of geometrical structural synthesis is creating the foundation to discover
the particular geometrical features and optimum structures by:
1) Generating set of main branches of platforms and structural groups.
2) Linking structural groups to the vacant branches of the manipulator.
3) Creating modular systems with multi DOF using successive layers of parallel
manipulators.
3.3.1 Generating Set of Main Branches of Platforms and Structural Groups
Consider the task of geometrical structural synthesis by generating a set of branches
for a parallel manipulator.
Definition: Position and orientation of ‘rigid body’ and its subsets ‘plane or line’,
‘cone surface’, ‘spherical or plane motion’ in space can be described by six, five, four and
three independent parameters respectively. A branch, taken as individual, must also has as
many DOF as independent parameters to be able to describe a rigid body or its subsets.
Let’s consider lower kinematic pairs only: one mobility p1, two mobility p2(p1- p1),
and three mobility p3(p1- p1- p1) where p1 = R (revolute) or P (prismatic) or H(screw), p2 =
C(cylindrical) or U(Universal), p3 = S(spherical) joints. On the base of interchangeability of
kinematic pairs we get common number of modification of platform branches (Table 3.1).
3.3.2 Linking Structural Groups to the Vacant Branches
In Figure 3.2a, a spatial parallel manipulator with a triangular platform is shown.
Each of three branches has two actuators. To place the actuators on the fixed base, a R-R-R
structural group is added to each branch.
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