Question:easy

Kutzback equation between degrees of freedom (n), number of links (l), number of joints (j) and number of higher pairs (h) of a mechanism having plane motion is given by

Show Hint

Recall how lower pairs and higher pairs each affect the degrees of freedom differently.
  • \(n = 3(l-1) - 2j - h\)
  • \(n = 3(l+3) - 2j - h\)
  • \(n = 3(l-3) - 2(j-h)\)
  • \(n = 3(l+1) - j + 2h\)
Show Solution

The Correct Option is A

Solution and Explanation

We can also arrive at the equation by counting degrees of freedom directly instead of recalling the formula.
Each unconnected rigid link moving in a plane has 3 degrees of freedom, two for translation and one for rotation. With $l$ links, and one of them fixed as the frame, the degrees of freedom available before adding any joints is $3(l-1)$.
Every lower pair, such as a pin joint or a sliding joint, removes 2 degrees of freedom because it only allows one relative motion between the two links it connects. With $j$ such joints, we subtract $2j$.
Every higher pair, such as a cam and follower or two gear teeth in contact, removes only 1 degree of freedom because it allows two relative motions, sliding and rolling, between the links. With $h$ such pairs, we subtract $h$.
Putting this together gives $n = 3(l-1) - 2j - h$, the same as option 1.
\[\boxed{n = 3(l-1) - 2j - h}\]
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