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

Using equations (3.4) and (3.6), we can solve structural synthesis task for parallel
structural groups for λ = 6 or λ = 3. If B = 0, equations (3.4) and (3.6) can be used for λi = 2,
3, 4, 5, 6 where we can describe single loop structural groups considering linear and angular
constraint kinematic pairs.
3.2 Structural Synthesis of Parallel Manipulators
Structural synthesis of parallel manipulators will now be considered. From equation
(3.4), (3.6) we may write the two objective functions of structural synthesis for parallel
structural groups as:
j = λ(N – C – B) (3.7)
n = (λ – 1)(N – C – B) (3.8)
also we have additional requirements in the form of equalities and inequalities as:
where
1) 3B ≤ N ≤ λB 2) B – 1 ≤ C ≤ 0.5N – 1 3) b = N – C
4) L = N – C – B 5) j = λL 6) jb = j / b 7) bv = N – 2C (3.9)
b: number of branches
jb: number of joints in a branch
bv: number of vacant branches.
For above conditions, we will give some explanations and reach to some conclusions:
1) The number of vacant branches is defined as the difference between number of
platforms joints and twice the number of intermediate branches between them. A
vacant branch is the branch that’s one end is connected to a platform and the other
end is vacant for connecting an actuator or connecting to ground.
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