Problem 4 (25 points (a) The figure below shows a planar parallel manipulator ca
ID: 1766043 • Letter: P
Question
Problem 4 (25 points (a) The figure below shows a planar parallel manipulator called a "variable geometry truss." Three actuated prismatic joints are used to control the position and orientation of the platform. The revolute joints at the end of each link are passive. Assume that that there are no actuator limits. E -So hot tr Use Gruebler's formula to calculate the number of degrees of freedom of the mechanism (b) Consider the Stewart platform shown in the following figure. Let 0i represent the displacement of the ith prismatic actuator. Use Gruebler's formula to compute the number of degrees of freedom of the mechanism.Explanation / Answer
Gruebler's equation:
>It is used to calculate the mobility. In order to control a mechanism,the no.of independent input motions must equal the no.of degrees of freedom of mechanism.
Degrees of freedom (DOF):
It is the no.of independent coordinates required to describe the position of body in space.
>An object in free space has six degrees of freedom.
>A fixed object has zero degrees of freedom.
Gruebler's equation:
No.of degrees of freedom of a mechanism is given by
F=3(n-1)-2l-h
Where,F=degrees of freedom
n=no.of links
=n2+n3+.........+nj
n2=no.of binary links
n3=no.of ternary links etc
l=no.of lower pairs, which is obtained by counting no. of joints
h=no. of higher pairs
In the given problem,
F=3(n-1)-2l-h
=3(4-1)-2(3)-0
=9-6-0
=3.
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