Consider a slider crank mechanism as shown:

Slider Crank Mechanism

> 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 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

Velocity of A relative to O

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

Velocity Diagram Slider Crank Mechanism (Part-1)

\boldsymbol{v_{ba}} is not known, but AB being a rigid link, 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.

Velocity Diagram Slider Crank Mechanism (Part-2)

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}.

Velocity Diagram Slider Crank Mechanism (Part-3)

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

Velocity Diagram Slider Crank Mechanism (Part-4)

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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Velocity Analysis – Slider Crank Mechanism (Graphical Method)

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