# Determining the Mobility (Degree of Freedom) Using Kutzbach Criterion Let's use the **Kutzbach criterion** (also known as Gruebler’s equation) for planar mechanisms: \[ M = 3(n-1) - 2j - h \] Where: - \( M \) = Mobility (degree of freedom) - \( n \) = Number of links (including the frame) - \( j \) = Number of lower pairs (single DOF joints, mainly revolute or prismatic) - \( h \) = Number of higher pairs (usually zero in simple mechanisms) --- ## Step 1: Count the Number of Links (\(n\)) From the diagram: - Ground (frame): 1 - Three moving links (each labeled "1" in the diagram): 3 \[ n = 4 \] --- ## Step 2: Count the Number of Joints (\(j\)) Look for revolute (rotational) or prismatic (sliding) joints: - Three revolute joints are clearly visible at the intersections. \[ j = 4 \] --- ## Step 3: Count the Number of Higher Pairs (\(h\)) No higher pairs are visible. \[ h = \] --- ## Step 4: Apply the Kutzbach Criterion \[ M = 3(n-1) - 2j - h \] \[ M = 3(4-1) - 2(4) - \] \[ M = 3(3) - 8 \] \[ M = 9 - 8 = 1 \] --- ## **Final Answer** **The mobility (degree of freedom) of the given mechanism is:** \[ \boxed{1} \] --- ### **Summary Table** | Parameter | Value | |-----------|-------| | n | 4 | | j | 4 | | h | | | **M** | **1** | --- **This mechanism is a single degree-of-freedom planar linkage.**