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

A simple analytical solution is obtained for inverse displacement problem and
implemented in a computer program called iMidas. The program can provide the user with the
required values of input corresponding to the desired path of motion. It is also possible to
visually verify the path from the three dimensional graphical simulation provided by the
program. From the data provided by the program, it is possible to reach some conclusions as:
• Manipulator becomes more sensitive to errors in actuators as the distance between
platform centroid and base frame increases, and vice versa.
• Accuracy of the manipulator, contributed by linear actuators, increases and the
useful workspace decreases as the construction parameter outer radius increases,
and vice versa.
• Accuracy of the manipulator, contributed by rotary actuators, increases and the
useful workspace decreases as the construction parameter inner radius increases,
and vice versa.
• Orientation capability of the platform decreases as the distance of the platform
from the base frame increase.
The inverse dynamics analysis is done using Lagrange-Euler’s equations of motion
and principle of virtual work. The equation of motion for the proposed manipulator, having
variable inertia factor, are derived. Finally, the inverse dynamics problem of the manipulator
is defined by six non-linear differential equations of second order.
Future research on this manipulator can be directed on forward and inverse velocity
and acceleration analysis, a complete workspace analysis, optimization of construction
parameters for specific tasks, stiffness analysis regarding different construction parameters
and identification of singular configurations. In addition, it will be a good practice to
endeavor solving the forward kinematics using artificial neural networks, using the exact
results obtained from inverse kinematics.
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