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

Let’s consider a 5 DOF parallel manipulator with a mobile pentagonal platform that’s
end-effector moving in subspace. To solve kinematic structural synthesis we conditionally
break one branch with 5 DOF and remaining branches to 6 DOF serial chains. Given
parameters are the position of the center of the platform and two parameters of normal of the
platform in subspace. For a 5 DOF serial manipulator, five parameters can be solved to find
one input and four joint variables. Secondly, we solve the position and orientation of
kinematic pairs lying on the mobile platform. The third step is to solve inverse task for each
remaining branch conditionally broken and constricted as serial manipulator with 6 DOF
(Figure 3.4b).
Consider a 4 DOF parallel manipulator in subspace with a mobile quadrilateral
platform. Known parameters for these manipulator are position of center of its mobile
platform ρ(x,y,z) and some angle φ, where e n ⋅ ei
= cos(ϕ ) ( e n is the normal of the moving
plane, e i is an arbitrary direction is space). These four parameters describe a cone surface in
the subspace. Algorithm consists also from these three steps. Firstly we solve the
conditionally broken branches as serial manipulators with 4 DOF. Secondly we solve position
and orientation of kinematic pairs laying on the mobile quadrilateral. Next we look to the
remaining three branches as serial manipulators with 6 DOF (Figure 3.4c).
Finally we will give the algorithm of structural kinematic synthesis for parallel
manipulator with 3 DOF having a mobile triangular platform (Figure 3.4d). The position of
the platform is defined by three parameters x, y and z. We take manipulator kind 2 x
(SUR)+(3R). Firstly, we conditionally break the 3 DOF branch as a serial manipulator.
Secondly find the position and orientation of the platform and than solve the inverse task of
two conditionally broken branches as serial manipulators with 6 DOF.
3.5 Computer Aided Structural Synthesis
At present, there isn’t any computer software that is specifically designed to focus on
the subject of structural synthesis. However, analysis software like MSC Visual Nastran
Desktop, Solid Works, Pro Engineer, AutoDesk Mechanical Desktop, etc. can be used to
verify the structural integrity, visualize the kinematic, static, dynamic, strength and vibration
considerations of mechanisms and manipulators.
In Appendix A, documentation of the computer program CASSoM is given. CASSoM
is a useful calculating tool, using the methods given in section 3.2.
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