The pantograph
A pantograph
Perhaps the most famous linkage is the pantograph. This is used to enlarge and reduce drawings. There are many different forms. Can you work out why it works?
Linkages are such an important topic that we cannot restrict attention just to those which only draw a straight line. Here are some others.
Perhaps the most famous linkage is the pantograph. This is used to enlarge and reduce drawings. There are many different forms. Can you work out why it works?
Another important simple linkage was used on drawing boards to keen the set square parallel to the edges of the board.
James Watt's linkage is often called a four bar linkage since it has three moving bars and a fixed base acting as the fourth. Mechanisms with four bars are the simplest possible, since three bars form a rigid triangle. In the following crossed parallelogram, what is the path of the intersection of the crossed bars?
Here is a rather intriguing motion from a four-bar mechanism.
AB=CD=5, BC=6, BP=PC=3.
This result concerns a general four-bar linkage AQ(P)RB, where the point of interest, P, is offset from the middle linkage QR. This is very similar to Roberts' linkage. The remarkable triple generation theorem says there are in fact three linkages that produce the locus of P.