b) The crank OA of a mechanism, as shown in the figure, rotates clockwise at 120 r.p.m. The lengths of various links are OA = 100 mm ; AB = 500 m ; AC = 100 mm and CD = 750 mm.

Find by instantaneous centre method:
1. Velocity of point C.
2. Velocity of slider D.
3. Angular velocities of the links AB and CD.

To find the answers using the instantaneous center method, we need to follow several steps:

Step 1: Draw the diagram of the mechanism and label all the given lengths.

Step 2: Locate the instantaneous center of rotation (ICR) for each moving link.

Step 3: Determine the velocity of point C using the ICR method.

Step 4: Determine the velocity of slider D using the ICR method.

Step 5: Determine the angular velocities of the links AB and CD using the velocity ratio principle.

Let's go through each step in detail:

Step 1: The given lengths are:
OA = 100 mm (length of crank)
AB = 500 mm (length of connecting rod)
AC = 100 mm (length of coupler)
CD = 750 mm (length of slider)

Step 2: To locate the ICR, extend the line of motion of each link and find the point where the lines of motion of two links intersect. Mark this point as the ICR. For this mechanism, the ICR for link OA and AB will be the same.

Step 3: To determine the velocity of point C, draw a line passing through the ICR and point C. The velocity of C can be found by multiplying the angular velocity of OA with the distance between ICR and point C. The formula to calculate the velocity is given by:
VC = ω * ICRC

Where:
VC = Velocity of point C
ω = Angular velocity of OA
ICRC = Distance between ICR and point C

Step 4: To determine the velocity of slider D, draw a horizontal line through the ICR. The velocity of D can be found by multiplying the angular velocity of AB with the distance between ICR and D. The formula to calculate the velocity is given by:
VD = ω * ICRD

Where:
VD = Velocity of slider D
ω = Angular velocity of AB
ICRD = Distance between ICR and D

Step 5: To determine the angular velocities of the links AB and CD, we need to use the velocity ratio principle. The ratio of the angular velocities is equal to the inverse ratio of the lengths of the links. The formula to calculate the angular velocities is given by:
ωAB / ωCD = DC / AB

Where:
ωAB = Angular velocity of AB
ωCD = Angular velocity of CD
DC = Length of CD
AB = Length of AB

Now let's proceed to calculate the answers.

Step 1: Draw the diagram and label the lengths as given.

Step 2: Locate the ICR for links OA and AB. (the point where the lines of motion of OA and AB intersect)

Step 3: To determine the velocity of point C, draw a line passing through the ICR (from Step 2) and point C. Measure the distance between ICR and C (ICRC). Multiply this distance by the angular velocity of OA (120 r.p.m converted to rad/s) to find the velocity of C.

Step 4: To determine the velocity of slider D, draw a horizontal line through the ICR (from Step 2). Measure the distance between ICR and D (ICRD). Multiply this distance by the angular velocity of AB (120 r.p.m converted to rad/s) to find the velocity of D.

Step 5: To determine the angular velocities of AB and CD, use the velocity ratio principle and the given lengths of AB and CD.

Please provide the figure or any additional information needed to proceed with the remaining steps.

To find the answers to these questions using the instantaneous center method, follow these steps:

1. Velocity of point C:
- Identify the point of contact between link AC and link CD. This point is called the instantaneous center of rotation for the two links.
- Draw a perpendicular line from point C to link AB. This line represents the velocity of point C.
- Measure the length of this line to find the velocity of point C.

2. Velocity of slider D:
- Identify the point of contact between link BC and link CD. This is the instantaneous center of rotation for the two links.
- Draw a perpendicular line from the instantaneous center to link CD. This line represents the velocity of slider D.
- Measure the length of this line to find the velocity of slider D.

3. Angular velocities of the links AB and CD:
- The angular velocity of link AB can be calculated using the equation: ΩAB = ωOA
- The angular velocity of link CD can be calculated using the equation: ΩCD = ωOA * (length of OA / length of CD)

Please note that to find the angular velocities, you need to know the angular velocity of crank OA, which is given as 120 r.p.m. You also need to convert this angular velocity to radians per second if necessary.

sorry, no diagram.