The Pneumatic Rivet Press animation is an excellent example of a linkage used to multiply force in a tool. In this application, shop compressed air, nominally at about 85 psi, is applied to a piston to produce a force of about 4500 pounds or two and one quarter tons. The maximum force developed at the tool is in excess of 60,000 pounds or thirty tons. This is multiplication by a factor of a little over thirteen.
Why do we need such a device? Before electric welding and high strength bolts became common, the usual method for joining steel structural members was by rivets. Rivets can be seen today in many older bridges, boilers, pressure vessels, railroad cars, and similar large steel structures. A rivet is a small steel component, shaped much like a simple bolt except that it has no threads. Two pieces of steel to be connected are clamped together with holes aligned through them allowing the rivet to be inserted from one side. Before insertion, the rivet is heated red hot to soften the rivet material. After insertion, the rivet is squeezed axially to deform the shank towards the head, thus creating a second head. As the rivet cools after being driven, the material of the rivet shrinks due to thermal contraction; this makes the joint even tighter and increases the friction between the two members thus joined. Rivets were used in large groups; a single rivet alone is never seen, so the means to drive many rivets was required. The rivet press is designed to provide the extreme force required to deform the rivet material, creating the second head.
How does it work? The central element of the linkage is the main link, shown in yellow. There are four simple links that attach to the main link to guide its motion. The silver-black tool that forms the rivet head is at the lower left, moving vertically in the brown frame. During the cycle, the tool bears down on the anvil that supports the rivet in order to expand the shank as a second head. The inclined piston moves to the right and upward because of the spring force as air is bled out of the cylinder (blue). This causes the tool to rise, opening a space to accept the rivet that is to be driven. When shop air pressure is admitted to the cylinder (red), the piston is forced to the left and down. As the piston moves to the left, the tool is forced down, creating the required rivet head.
This tool is too heavy to be carried by hand, so it is typically suspended on a chain from an overhead location. With the weight of the tool supported on the chain, the tool can be moved from one location to the next, driving a rivet at each location.
Although rivets are no longer used in very many applications, the idea of force multiplication remains very much in use. This remarkable linkage provides an effective means to accomplish that end. The means to mathematically analyze this linkage and many others like it are found in the textbook, Mechanics of Machines, 2nd edition, soon to be available through the mekanizmalar.com web site in PDF format without charge.