Notes on Velocity Analysis in Mechanisms

Importance of Velocity Analysis

• Crucial for the proper design of mechanisms.
• Focus on variation of outlet link velocity for a specified inlet velocity.

Key Concepts in Velocity Analysis

Concept 1: Rigid Body Behavior

• Rigid Body Definition: Cannot elongate or contract in any direction.
• Velocity Components:
  • Two points in a rigid body can have different velocities.
  • Velocity components parallel to the line connecting the points must be equal.
  • If component velocity of point B > point A: Link elongates (impossible).
  • If component velocity of point A > point B: Link contracts (impossible).
• Conclusion:
  • Relative velocity between any two points in a rigid body should be perpendicular to the line connecting them.

Concept 2: Mating Surfaces

• Mating Pairs: Surfaces will not penetrate.
• Common Normal: The line representing the common normal for both links.
• Velocity Components:
  • The same point on different links can have different velocities.
  • Velocity components along the common normal must be equal to avoid penetration or detachment.
• Conclusion:
  • The relative velocity should be perpendicular to the common normal.

Application of Concepts

Example 1: Four-Bar Linkage

• Given: Input angular velocity.
• Goal: Find outlet velocity.
• Methodology:
  • Bar in the middle cannot expand or contract.
  • Determine magnitude and direction of velocity at point 1 using known angular velocity.
  • Use Concept 1 to find the magnitude of velocity at point 2 (ensure perpendicularity).
  • Deduce angular velocity of the link from point 2's velocity.

Example 2: Cam Mechanism

• Given: Angular velocity of the first cam.
• Goal: Find angular velocity of the second cam.
• Methodology:
  • Identify mating point on both cams.
  • Use known velocity direction and magnitude of the first cam's mating point.
  • Apply Concept 2: Since links cannot penetrate, ensure relative velocity is perpendicular to the common normal.
  • Find the magnitude of V2, leading to the angular velocity of the second cam.

Conclusion

• The principles of velocity analysis can be applied to analyze various mechanisms effectively.
• Understanding these concepts is essential for successful design and analysis of mechanical systems.