The number of degree of freedom of a planar linkage with 8 links and 9...
To determine the number of degrees of freedom of a planar linkage with 8 links and 9 simple revolute joints, we need to analyze the constraints imposed by the joints and the number of independent variables that can define the configuration of the mechanism.
Joints in a Planar Linkage:
A planar linkage consists of links connected by joints, which allow relative motion between the links. In this case, we have 9 simple revolute joints, which means that each joint allows rotation about a single axis.
Degrees of Freedom:
The degrees of freedom (DOF) of a mechanism represent the number of independent variables required to define its configuration. In a planar mechanism, the DOF is given by:
DOF = 3n – 2j - h
where n is the number of links, j is the number of joints, and h is the number of higher pairs (other than revolute). In this case, we have:
n = 8 (number of links)
j = 9 (number of revolute joints)
h = 0 (no higher pairs)
Substituting these values into the equation, we get:
DOF = 3(8) - 2(9) - 0
= 24 - 18
= 6
However, in a planar mechanism, there are three constraints that restrict the motion of the mechanism:
1. Grounding constraint: One link is usually fixed to the ground, which restricts its motion completely. This eliminates two degrees of freedom.
2. Loop closure constraint: The links in a closed loop mechanism are constrained by the loop closure equation, which relates the relative positions and orientations of the links. This equation imposes an additional constraint and eliminates one degree of freedom.
Therefore, the actual number of degrees of freedom for the given planar linkage is:
DOF_actual = DOF - 2 - 1
= 6 - 2 - 1
= 3
Hence, the correct answer is option 'C', which states that the number of degrees of freedom is 3.