Explanation:

When a slider moves on a fixed link with a curved surface, the instantaneous center lies at the center of curvature. Let's understand this concept in detail.

Definition: The instantaneous center is the point in a mechanism that has zero velocity at any given instant. It is the point about which all other points on the mechanism are moving or rotating.

Understanding the concept:

When the slider moves on a fixed link with a curved surface, it experiences both linear and angular motions. The slider moves along the curved surface, which causes linear motion, and it also rotates about a point, which causes angular motion.

Centers of Curvature:

The centers of curvature are the centers of the circles that best fit the curve at any given point. These centers are located on the normal line to the curve at that point. In other words, the centers of curvature represent the instantaneous centers of rotation for the slider at different positions along the curved surface.

Instantaneous Center:

The instantaneous center is the intersection point of the centers of curvature for the slider at different positions. It is the point where the linear and angular velocities of the slider are zero.

Location of Instantaneous Center:

In the case of a curved surface, the instantaneous center lies at the center of curvature. It is the point about which the slider is both moving linearly and rotating.

Significance:

The knowledge of the instantaneous center is crucial for understanding the motion and forces in mechanisms. It helps in analyzing and designing various mechanical systems, such as linkages, gears, and cams.

Conclusion:

When the slider moves on a fixed link with a curved surface, the instantaneous center lies at the center of curvature. This point represents the intersection of the centers of curvature for the slider at different positions along the curved surface. Understanding the concept of the instantaneous center is essential for analyzing the motion and forces in mechanical systems.