Error Modeling and Design Optimization of Parallel Manipulators

Parallel mechanism based robotic manipulators feature higher performance in terms of
accuracy, rigidity, speed and payload over the serial manipulators and they have found
the industrial applications in many elds.
Nevertheless, the design and application of parallel manipulators face many challenges
due to their highly nonlinear behaviors, thus, the parameter and performance analysis,
especially the accuracy and stiness, are particularly important. Toward the requirements
of robotic technology such as light weight, compactness, high accuracy and low
energy consumption, utilizing optimization technique in the design procedure is a suitable
approach to handle these complex tasks.
As there is no unied design guideline for the parallel manipulators, the study described
in this thesis aims to provide a systematic analysis for this type of mechanisms in the
early design stage, focusing on accuracy analysis and design optimization. The proposed
approach is illustrated with the planar and spherical parallel manipulators. The
geometric design, kinematic and dynamic analysis, kinetostatic modeling and stiness
analysis are also presented.
Firstly, the study on the geometric architecture and kinematic problem of the planar
and spherical parallel manipulators is carried out. The kinematic problem is the basis
for further study of mechanisms, which includes the development of the kinematic closure
equation, derivation of the kinematic Jacobian matrix, input-output expression of
velocity and accelerations, dynamic modeling etc.
Next, the rst-order dierential equation of the kinematic closure equation of planar
parallel manipulator is obtained to develop its error model both in Polar and Cartesian
coordinate systems. The established error model contains the error sources of actuation
error/backlash, manufacturing and assembly errors and joint clearances. From the error
prediction model, the distributions of the pose errors due to joint clearances are mapped
within its constant-orientation workspace and the correctness of the developed model is
validated experimentally.
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Additionally, using the screw theory and virtual spring approach, a general kinetostatic
model of the spherical parallel manipulators is developed and validated with Finite Element
approach. This model is applied to the stiness analysis of a special spherical
parallel manipulator with unlimited rolling motion and the obtained stiness isocontours
show an overall image of the stiness. The elastic deformation of the center of rotation
or center shift for spherical parallel manipulators cannot be neglected. Moreover, the positioning
accuracies of the spherical parallel manipulators with dierent structures were
compared. The comparison reveals the in
uence of link structures on the orientation
accuracy.
Finally, with the previously developed kinematic, kinetostatic and dynamic models, a
multiobjective optimization problem is formulated to optimize the structural and geometric
parameters of the spherical parallel manipulator. The proposed approach is
illustrated with the design optimization of the proposed spherical parallel manipulator
that aims to minimize the mechanism mass and to maximize the global conditioning
index to enhance both kinematic and dynamic performances. Behind the implemented
study case, the proposed method oers a great
exibility to select any criterion as an objective
function based on requirements, as dierent kinds of performances ranging from
kinematics, statics to dynamics are employed to formulate this systematic approach for
design optimization.