## STRAIGHT LINE MECHANISMS

**Straight line motion mechanisms**

Straight line motion mechanisms are mechanisms, having a point that moves along a straight line, or nearly along a straight line, without being guided by a plane surface.

**Condition for exact straight line motion:**

If point B (fig.1.40) moves on the circumference of a circle with center O and radius OA, then, point C, which is an extension of AB traces a straight line perpendicular to AO, provided product of AB and AC is constant.

**Fig.1.40: Condition for exact straight line motion**

Locus of pt.C will be a straight line, ┴ to AE if, is constant

**Proof:**

**Peaucellier exact straight line motion mechanism:**

**Fig.1.41: Peaucellier exact straight line motion mechanism**

Here, AE is the input link and point E moves along a circular path of radius AE = AB. Also, EC = ED = PC = PD and BC = BD. Point P of the mechanism moves along exact straight line, perpendicular to BA extended.

*To prove B, E and P lie on same straight line:*

Triangles BCD, ECD and PCD are all isosceles triangles having common base CD and apex points being B, E and P. Therefore points B, E and P always lie on the perpendicular bisector of CD. Hence these three points always lie on the same straight line.

*To prove product of BE and BP is constant.*

In triangles BFC and PFC,

But since BC and PC are constants, product of BP and BE is constant, which is the condition for exact straight line motion. Thus point P always moves along a straight line perpendicular to BA as shown in the fig.1.41.

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**Approximate straight line motion mechanism: **A few four bar mechanisms with certain modifications provide approximate straight line motions.

**Robert’s mechanism**

**Fig.1.42: Robert’s mechanism**

This is a four bar mechanism, where, PCD is a single integral link. Also, dimensions AC, BD, CP and PD are all equal. Point P of the mechanism moves very nearly along line AB.