Test: Velocity & Acceleration Analysis - 1 - Mechanical Engineering MCQ

velocity = lω

  = ω x AB

If three plane bodies have relative motion among themselves, their I-center must lie on a straight line, this is known as Kennedy’s theorem.

In a sliding motion, the I-center lies at infinity in a direction perpendicular to the path of motion of the slider. The sliding motion is equivalent to a rotary motion of the links with the radius of curvature as infinity.

E i s instantaneous center for the link A B and C D and angular velocity for the point B and C would be same about E

• The instantaneous axis is a line perpendicular to the plane of motion passing through the instantaneous center.

• The locus (path traced) of this axis during motion is termed the axode.

• Centrodes (space or body) refer to the locus of the instantaneous center, not the axis.

The correct term for the locus of the instantaneous axis is axode.

The instantaneous center of rotation for a circular disc that is rolling along a straight path is located at the point where the disc touches the surface. This point is crucial in understanding the motion of the disc.

• The instantaneous center is the point in the rolling body that remains momentarily at rest.
• As the disc rolls, it rotates around this point of contact with the ground.
• This concept helps to analyse the motion of the disc more effectively.
• In this case, the point of contact serves as the pivot for the disc’s rotation.

Thus, when considering the motion of a rolling disc, it is important to note that the center of rotation is not at the centre of the disc or its centre of gravity, but rather at the point where it makes contact with the surface.

A centrode is the locus of the I-center of a plane body relative to another plane body for the range of motion specified or during a finite period of time.
Space centrode (or fixed centrode) is the locus of the I-center of the moving body relative to the fixed body.
Body centrode (or moving centrode) is the locus of the I-center of the fixed body relative to the movable body.

The space centrode of a circular disc that rolls along a straight path can be understood through the following points:

• The term centrode refers to the path traced by the centre of a rolling object.
• As the circular disc rolls, the motion creates a predictable trajectory.
• For a circular disc, this trajectory is a straight line due to the uniform rolling motion.
• The concept can be visualised as the disc continuously making contact with the surface beneath it.

Thus, the space centrode of a circular disc rolling on a straight path is a straight line.