Subject: Kinematics of Machinery

Topic: Special Mechanism

Difficulty: High

A pantograph is an instrument used to reproduce to an enlarged or reduce scale and as exactly as possible the path describes by a given point.

It consists of a jointed parallelogram ABCD as shown in fig. it is made up of bars connected by turning pairs. The bar BA and BC are extended to O and E respectively, such that

$\frac{OA}{OB}=\frac{AD}{BE}$

Thus, for relative positions of the bar the triangles OAD and OBE are similar and the points O, D, and E are in one straight line. It may be proved that point E traces out the same path as described by point D.

From similar triangles OAD and OBE, we find that

$\frac{OD}{OE}=\frac{AD}{BE}$

Let point O fixed and the points D and E move to some new positions D' and E'. Then

$\frac{OD}{OE}=\frac{OD'}{OE'}$

A little consideration will show that the straight line DD’ is parallel to the straight line EE'.

Hence, if O is fixed to the frame of the machine by means of a turning pair and D is attached to a point in the machine which has rectilinear to the frame, then E will also trace out a straight line path. Similarly, if E is constrained to move in a straight line, then D will trace out a straight line parallel to the former.

A pantograph is mostly used for the reproduction of plane areas and figures such as maps, plans etc. on enlarged or reduced scales. It is sometimes, used as an indicator rig in order to reproduce on a small scale the displacement of the crosshead and therefore of the piston of a reciprocating steam engine. It is also used to guide cutting tools. A modified form of pantograph is used to collect power at the top of an electric locomotive.