Short Answer:

The instantaneous center of rotation is a point in a moving body or mechanism around which all other points move in a circular path at a particular instant of time. At that instant, this point has zero velocity. It helps in analyzing the motion of different links and parts of a mechanism by simplifying their rotational movement.

In simple terms, the instantaneous center acts as a temporary axis of rotation that changes its position as the mechanism moves. It is a very useful concept for studying the relative motion and velocity of different components in machines.

Detailed Explanation:

Instantaneous Center of Rotation

The instantaneous center of rotation (ICR) or instantaneous center of zero velocity (IC) is a fundamental concept in the study of kinematics of mechanisms and moving bodies. It is used to simplify complex planar motions into simple rotational motion about a single point at a specific instant. In mechanical systems, where links move relative to one another, this concept helps in determining the velocity of any point on a link quickly and accurately without involving long calculations.

1. Definition and Meaning

The instantaneous center of rotation can be defined as:

“The point in or outside a moving body about which all other points of the body appear to rotate at a particular instant.”

At that instant, this point has zero velocity relative to the fixed frame or another link. Therefore, all other points in the body move as if they are rotating around this center.

For a body in general plane motion, every instant of time has one such point, which may change its position as the motion continues. Hence, it is called instantaneous center rather than a permanent one.

2. Importance of Instantaneous Center

The concept of instantaneous center is extremely useful in mechanics because it allows engineers to study the velocity of moving links without using complicated equations. Once the instantaneous center is located, every point on the link can be treated as rotating around that center with an angular velocity .

Thus, the velocity  of any point on the link is given by:

where,
= angular velocity,
= distance of the point from the instantaneous center.

This makes it easier to analyze mechanisms such as four-bar linkages, slider-crank mechanisms, and other complex motion systems.

3. Types of Instantaneous Centers

There are generally two types of instantaneous centers in planar mechanisms:

1. a) Fixed Instantaneous Center:
   This is a point that remains stationary throughout the motion, such as the center of a rotating wheel fixed to the ground.
2. b) Moving Instantaneous Center:
   This point changes its position as the body moves. For example, in a rolling wheel, the point of contact with the ground keeps shifting continuously, acting as a moving instantaneous center at every instant.
3. Location of Instantaneous Center

The instantaneous center of rotation can be located using geometrical methods. One common and simple method is the perpendicular method:

• Draw the direction of velocities of two points on the moving body.
• Draw perpendiculars to these velocity directions.
• The point where the perpendiculars intersect is the instantaneous center of rotation.

This method helps in visualizing how different parts of a mechanism move at an instant.

5. Example: Rolling Wheel

Consider a wheel rolling on the ground without slipping. At any given instant, the point of contact between the wheel and the ground has zero velocity because it is momentarily at rest relative to the surface. Therefore, that point acts as the instantaneous center of rotation for the wheel.

All other points on the wheel move in circular paths about this center. The topmost point of the wheel moves with the highest velocity, which is twice the linear velocity of the center of the wheel.

6. Instantaneous Center in Mechanisms

In mechanisms such as four-bar linkages or slider-crank mechanisms, instantaneous centers help determine the motion relationship between different links. For example:

• In a four-bar mechanism, there are multiple instantaneous centers corresponding to each pair of links.
• Using these centers, the velocity ratio between links can be found using Kennedy’s theorem, which states that for any three bodies in relative motion, their three instantaneous centers lie on a straight line.

Thus, by locating instantaneous centers, engineers can easily determine velocity ratios and directions without lengthy vector calculations.

7. Mathematical Relationship

The velocity of any point on the body can be found using:

 

where  and  are points on the same link and ,  are their respective distances from the instantaneous center.

Since the angular velocity  is the same for the whole link, the ratio of their velocities is equal to the ratio of their distances from the instantaneous center:

This equation helps in solving problems of velocity analysis in mechanisms.

8. Applications of Instantaneous Center

The concept of instantaneous center is applied in various fields of mechanical engineering:

• Kinematic analysis of linkages – used to find velocities of different links in mechanisms.
• Design of automobiles – helps in understanding wheel motion and steering geometry.
• Robotics – useful in analyzing and controlling movement of robotic arms.
• Machinery design – assists in studying velocity transmission between interconnected parts.
• Dynamics of rotating systems – simplifies calculation of velocities and angular motions.

9. Graphical Significance

In graphical kinematics, drawing the instantaneous center makes it easier to visualize motion. Once the center is marked, the velocity direction of any point on the body can be drawn tangential to the circle about that point.

Conclusion:

The instantaneous center of rotation is the temporary point about which a body appears to rotate at any given instant. It has zero velocity at that moment, while all other points move in circular paths around it. This concept simplifies the study of planar motion and is essential in analyzing velocities of various links in mechanisms. Understanding and locating the instantaneous center is vital for mechanical engineers to analyze and design efficient mechanical systems and motion mechanisms.