Klein's construction to determine velocity and acceleration of , single slider crank mechanism.

*Klein's construction to determine velocity and acceleration       

 of single slider crank mechanism.*

Let OC is the Crank & PC is the connecting Rod of a reciprocating steam Engine.

Let the crank makes an angle with the line of strokes PO ,And rotates with uniform angular velocity in rad/sec in a clock wise direction.

Diagram-

First of all draw OP perpendicular to OP,that’s intersect to line pc produce at M.

Then the TRAINGLE ‘’OCM ‘’ produced that’s known as kleins velocity diagram.

We have already discussed that the velocity diagram for given configuration is a triangle OCP as shown in Fig.

If this triangle is rotated through 90°, it will be a triangle oc1 p1, in which oc1 represents VCO  and is parallel to OC,

 op1 represents VPO velocity of P with respect to O or velocity of cross-head or piston P) and is perpendicular to OP, and c1p1 represents VPC and is parallel to CP.

A little consideration will show that the triangles oc1p1 and OCM are similar. Therefore, 

Klien’s acceleration diagram:

The Klien’s acceleration diagram is drawn as discussed below: 

1. First of all, draw a circle with C as centre and CM as radius.

2. Draw another circle with PC as diameter. Let this circle intersect the previous circle at K and L.

3. Join KL and produce it to intersect PO at N. Let KL intersect PC at Q. This forms the quadrilateral CQNO, which is known as Klien’s acceleration diagram.

We have already discussed that the acceleration diagram for the given configuration is as shown in Fig. We know that (i) o'c' represents CO  and is parallel to CO;

(ii) c'x represents PC and is parallel to CP or CQ;

 (iii) xp' represents PC at and is parallel to QN (because QN is perpendicular to CQ); and

(iv) o'p' represents PO and is parallel to PO or NO. A little consideration will show that the quadrilateral o'c'x p' is similar to quadrilateral CQNO .