Topic: Theory of Machines
Find the total number of degrees of freedom for following system. Assume rolling without slipping.
- A. 0
- B. 1
- C. 2
- D. Cannot be determined
Answer: B. 1
Explanation: Applying Kutzbach's criterion: $F = 3(n-1) - 2j - h$.
Number of links $n = 4$ (Ground=1, oscillating left arm=2, connecting rod=3, wheel=4).
The joints ($j$) are 3 pin joints (ground-arm, arm-rod, rod-wheel) and 1 rolling contact without slipping. A rolling contact without slipping removes 2 degrees of freedom (constrains vertical movement and relates horizontal translation strictly to rotation), making it act as a lower pair ($j=1$).
$F = 3(4-1) - 2(4) = 9 - 8 = 1$.