Degree of Freedom (Kutzbach Criterion)

[unknown619a]

Homework Statement

To figure out the degree of freedom of a mechanism in 3D space. The resulting diagram is in the attachment. It consists of 6 revolute joints and 1 prismatic joint. All joints act in the z-x plane besides joint 1 which revolves around the z axis (i.e moves the mechanism into the y plane)

Homework Equations

M=6(n-1-j)+∑fi-Ʃfp
n = number of links
j= number of joints
fi= Total degree of freedom of the joints
fp= Reduandant/idle degree of freedom

The Attempt at a Solution

with n=7 and j=6 and fi=6 i get 6 degree of freedom. Even though i know the answer should be 4 degree of freedom which means that fp=2 however i do not know how to explain this which i am required to do. My initial thoughts were to say that since joints 2 and 4 both provide the same motion that one of them is redundant. Am i on the right track. Any help would be appreciated

 

[LightHero]

. ![enter image description here][1]Since there are 6 revolute joints and 1 prismatic joint, the total degree of freedom is 6(6-1-6)+6=6. However, since joints 2 and 4 provide the same motion, one of them is redundant. Therefore, the actual degree of freedom is 6-2=4.