Lecture Notes: Mechanisms and Degrees of Freedom

Introduction to Mechanisms

• Focus on understanding the degrees of freedom for different mechanisms.
• Use of Kurzweil criterion (or equation):
  • Degrees of Freedom (f) = 3(n - 1) - 2p1 - p2
  • n = number of links
  • p1 = number of lower pairs with one degree of freedom
  • p2 = number of higher pairs with two degrees of freedom

Example Mechanism Analysis

First Mechanism

• Count Links:
  • Fixed link = 1
  • Additional links: 2, 3, 4, 5
  • Total links (N): 5
• Lower Pairs (P1):
  • Five joints (1, 2, 3, 4, 5)
• Higher Pairs (P2):
  • One joint due to slippage (1)
• Calculation:
  • f = 3(5 - 1) - 2(5) - 1
  • f = 12 - 10 - 1 = 1
• Result: Degree of freedom = 1

Second Mechanism

• Count Links:
  • Links: 1, 2, 3 (ternary), 4, 5, 6, 7
  • Total links (N): 7
• Lower Pairs (P1):
  • Eight joints (1, 2, 3, 4, 5, 6, 7, 8)
• Higher Pairs (P2):
  • None
• Calculation:
  • f = 3(7 - 1) - 2(8)
  • f = 18 - 16 = 2
• Result: Degree of freedom = 2

Third Mechanism

• Count Links:
  • Links: 1, 2, 3
  • Total links (N): 3
• Lower Pairs (P1):
  • Two joints
• Higher Pairs (P2):
  • One joint with line or point contact
• Calculation:
  • f = 3(3 - 1) - 2(2) - 1
  • f = 6 - 4 - 1 = 1
• Result: Degree of freedom = 1

Conclusion

• Practice calculating degrees of freedom for various mechanisms to understand them better.
• End of chapter on introduction to mechanisms.
• Next chapter: Kinematic analysis of mechanisms, starting with velocity analysis.