velocities in four-bar chain

VELOCITIES IN FOUR-BAR CHAIN

Fig.2.4(a) shows a four-bar chain ABCD in which AD is fixed and BC is the coupler. AB is the driver rotating at an angular speed of @ rad/s in the clockwise direction. It is required to draw the velocity diagram of this configuration.

Procedure

Step 1: Configuration diagram: First of all, draw the configuration diagram, to some suitable scale, as shown in Fig.2.4(a).

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

Step 3: Velocity diagram: Now draw the velocity diagram, as shown in Fig.2.4(b), using the procedure given below.

1. Since the link AD is fixed, the velocity of points A and D are zero and they are represented by one point (a, d) in the velocity diagram.

2. From point a, draw vector ab perpendicular to BA, to some suitable scale, to represent the velocity of B with respect to A (i.e., v_BА or v_B) such that

vector ab = v_BA = v_B

3. From point b, draw vector bc perpendicular CB to represent the velocity of C with respect to B (i.e., v_CB).

4. Now from point d or a, draw vector de perpendicular to CD to represent the velocity of C with respect to D (i.e., v_CD or v_C).

5. The vectors bc and dc intersect at point c. The vector dc = v_CD = v_C.

Step 4: Velocity of various links: By measurement of vectors ac and bc, the velocities of link CD (v_CD) and link CB (v_CB) can be determined.

The angular velocity of links BC and CD can be determined by using the relations