- Practice · 5 marks
Instantaneous centre versus relative velocity method
Short answer
Relative velocity method uses vector addition and handles accelerations; instantaneous centre method treats motion as pure rotation about the IC, gives quick results for a single link but not for accelerations. Centrode is the locus of the IC: fixed centrode on the frame, moving centrode on the moving body. Types: fixed IC (crank pivot), permanent IC (crank pin), neither fixed nor permanent (coupler-frame IC).
Differentiate between the relative velocity method and the instantaneous centre method of velocity analysis. Define centrode and state the three types of instantaneous centres with examples.
Comparison
| Point | Relative velocity method | Instantaneous centre method |
|---|---|---|
| Basis | (vector addition) | Motion treated as pure rotation about the IC |
| Output | All velocities (and angular velocities) of the mechanism | Velocities of points of one link at a time |
| Accuracy | Good; the polygon is drawn once | Depends on locating ICs (they may fall far away) |
| Complicated mechanisms | Suitable; also extends to accelerations | Becomes long as the number of ICs grows |
| Acceleration | The same method continues with an acceleration polygon | Not applicable |
| Speed | Needs a polygon for each position | Quick for a single link and position |
Centrode
The locus of the instantaneous centre of a moving body is called its centrode. The path of the IC in the fixed body is the fixed centrode; its path in the moving body is the moving centrode. The motion of the body is equivalent to the moving centrode rolling on the fixed centrode without slipping.
Example: for a ladder sliding down a wall, the fixed centrode is a circular arc (centred at the corner, with radius equal to the ladder length), and the moving centrode is a semicircle with the ladder as its diameter.
Types of instantaneous centres
- Fixed IC: remains in the same place for all positions of the mechanism, for example the IC of the crank and frame at the crank pivot.
- Permanent IC: changes its place as the mechanism moves, but is always at the pin joint between two links, for example the crank pin (crank and connecting rod).
- Neither fixed nor permanent: not at a joint, and its position changes with the configuration, for example the IC of the connecting rod and the frame of a slider crank.
✓ Answer checked by Claude Opus 5.5 (high effort)
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