velocities in slider-crank mechanism

VELOCITIES IN SLIDER-CRANK MECHANISM

A slider-crank mechanism is shown in Fig.2.5(a). Crank OA rotates clockwise with angular velocity o rad/s. It is required to draw the velocity diagram.

Procedure

Step 1: Configuration diagram: First of all, draw the configuration diagram, to some suitable scale, as shown in Fig.2.5(a).

Step 2: Velocity of input link: When length of input link OA and its angular velocity ω_OA are known, then the velocity of the input link (i.e., crank OA) is given by

Step 3: Velocity diagram: Now draw the velocity diagram, as shown in Fig.2.5(b), using the procedure given below.

1. From any arbitrary point o, draw vector oa perpendicular to the link OA, to some suitable scale, such that oa = v_AO = ω • OA.

2. Since AB is a rigid link, therefore the velocity of B with respect to A is perpendicular to AB. Now from point a, draw vector ab perpendicular to AB to represent the velocity of B with respect to A (i.e., v_BA).

3. Since the velocity of slider B relative to O (i.e., v_BO) is along the line of stroke OB, so from point o, draw vector ob parallel to OB.

4. The vectors ab and ob intersect at point b.

Step 4: Velocity of various links:

By measurement, from the velocity diagram, we get

Velocity of the connecting rod, v_BA = vector ab

and Velocity of the slider, v_BO = vector ob

The angular velocity of the connecting rod AB (@AB) can be determined using the relation

The direction of vector ba determines the sense of ω_BA which shows that it is counter clockwise.

Note

The velocity of any point C located on the connecting rod AB, may be determined with the help of the below relation.

Thus point c can be located as shown in Fig.2.5(b). Join o and c. Vector oc represents the absolute velocity of point C (v_C).