Question

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

• A. \(n = 3(l-1) - 2j - h\)
• B. \(n = 3(l+3) - 2j - h\)
• C. \(n = 3(l-3) - 2(j-h)\)
• D. \(n = 3(l+1) - j + 2h\)

Hint:

Recall how lower pairs and higher pairs each affect the degrees of freedom differently.

Answer 1

The Correct Option is A

Step 1: Kutzback's equation gives the degree of freedom, or mobility, of a planar mechanism in terms of the number of links, lower pairs and higher pairs.

Step 2: The standard form of the equation is \(n = 3(l-1) - 2j - h\), where \(l\) is the number of links, \(j\) is the number of joints or lower pairs, and \(h\) is the number of higher pairs.

Step 3: This form builds on Grubler's equation for planar mechanisms, extended by Kutzback to also account for higher pairs, each of which removes only one degree of freedom compared to two for a lower pair.

This matches option 1 exactly.