--- title: "Instantaneous centre versus relative velocity method" subject: "Theory of Mechanism and Machine I" chapter: 7 key: "semester_6/theory_of_mechanism_and_machine_i:instantaneous-centre-versus-relative-velocity" source: https://www.bctengineer.com/q/semester_6/theory_of_mechanism_and_machine_i/instantaneous-centre-versus-relative-velocity site: BCT Engineering --- # Instantaneous centre versus relative velocity method Theory of Mechanism and Machine I · Chapter 7: Kinematic Analysis of Mechanisms - Asked in: year not given, 5 marks - Video: [Velocity of points in mechanism | Instantaneous center methods and relative velocity methods | KoM](https://www.youtube.com/watch?v=tRUTzBY79uE) — Mahesh Gadwantikar - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_6/theory_of_mechanism_and_machine_i/instantaneous-centre-versus-relative-velocity - Whole chapter: https://www.bctengineer.com/md/semester_6/theory_of_mechanism_and_machine_i/chapter-7 ## Question 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. ## 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). ## Answer #### Comparison | Point | Relative velocity method | Instantaneous centre method | |---|---|---| | Basis | $\vec v_B = \vec v_A + \vec v_{BA}$ (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 1. **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. 2. **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). 3. **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. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. Which statement correctly contrasts the two methods? A. The IC method also extends to accelerations B. The relative velocity method extends to accelerations by an acceleration polygon; the IC method does not C. The relative velocity method gives only one link at a time D. Neither can be used for complex mechanisms Answer: B. The relative velocity method continues with an acceleration polygon; the IC method is not applicable to accelerations. (Key point: Method comparison) 2. What is a centrode? A. The path of the centre of mass B. The locus of the instantaneous centre C. The line joining two pivots D. The circle through three pins Answer: B. A centrode is the locus of the instantaneous centre; fixed and moving centrodes roll on each other without slipping. (Key point: Centrode definition) 3. For a ladder sliding down a wall, the moving centrode is: A. A circular arc of radius equal to the ladder length B. A straight line along the wall C. A semicircle on the ladder as diameter D. The floor Answer: C. The fixed centrode is a circular arc of radius L; the moving centrode is a semicircle on the ladder as diameter. (Key point: Ladder centrodes) 4. Which IC is neither fixed nor permanent? A. Crank and frame at the crank pivot B. Crank and connecting rod at the crank pin C. Rocker and frame at its pivot D. Connecting rod and frame of a slider crank Answer: D. Its position and type change with configuration, unlike a fixed IC or a pin-joint permanent IC. 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