Consider a slider crank mechanism as shown:

**> **The crank *OA *is moving with uniform angular velocity ω radians/second in the counter-clockwise direction.

**> **At point *B*, the slider moves on the fixed guide *G.*

* > AB* is the coupler joining

*A*and

*B.*

**We are interested in finding the velocity of the slider at B.**

We can write the velocity vector equation for point *B* as:

\boldsymbol{v_{bo} = v_{ba} + v_{ao}}

\boldsymbol{v_{bo}} is the velocity of *B* relative to *O*.

\boldsymbol{v_{ba}} is the velocity of *B* relative to* A*.

\boldsymbol{v_{ao}} is the velocity of *A* relative to *O*.

Since the points *O *and *G* are on a fixed link with zero relative velocity between them,

\boldsymbol{v_{bo} = v_{bg}}

So, in the velocity vector equation for the point *B*, we can replace the velocity of *B* relative to *O* by the velocity of *B* relative to* G*.

\boldsymbol{v_{bg} = v_{ba} + v_{ao}}

To draw the velocity diagram, we will represent \boldsymbol{v_{bg}} by the vector \boldsymbol{gb}, \boldsymbol{v_{ba}} by the vector \boldsymbol{ab} and, \boldsymbol{v_{ao}} by the vector \boldsymbol{oa}.

\boldsymbol{gb = ab + oa}

\boldsymbol{v_{ao}} is completely known,

\boldsymbol{v_{ao} = \omega.|OA|} **; ⊥ to OA**

We draw the velocity vector \boldsymbol{v_{ao}} equal to its magnitude \boldsymbol{\omega.OA} at some convenient scale with its root at point *O *and its direction perpendicular to the link *OA.*

\boldsymbol{v_{ba}} is not known, but *AB* being a rigid link, *B *can’t move relative to *A* along the link *AB. *Therefore, its velocity direction can only be perpendicular to the link *AB. *So, in the velocity diagram, we draw a line through point *A* perpendicular to the link *AB*.

To locate the point \boldsymbol{b} on this line, we draw a line parallel to the motion of the slider through the point *G*. This line intersects the previous line and the point of intersection gives us the point \boldsymbol{b}.

We indicate the directions on the velocity diagram in accordance with the vector equation, \boldsymbol{v_{bg} = v_{ba} + v_{ao}}

**> **The vector \boldsymbol{gb} indicates the velocity of the slider *B* relative to the guide *G*.

The slider moves towards left as indicated by the vector \boldsymbol{gb}.

**> **As indicated by the vector diagram, for the given configuration, the coupler *AB* has an angular velocity in the clockwise direction.

\boldsymbol{\omega_{ba} = \frac{|v_{ba}|}{|AB|}}, clockwise direction

We can measure \boldsymbol{v_{ba}} from the velocity diagram.

This completes the velocity analysis of the slider crank mechanism.

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An excellent post, congratulations !!