KINEMATICS OF MACHINES Four bar chain mechanism-Analysis & Application

History Archimedes applied geometry to the study of the lever. Into the 1500s the work of Archimedes and Hero of Alexandria were the primary sources of machine theory. It was Leonardo da Vinci who brought an inventive energy to machines and mechanism. In the mid-1700s the steam engine was of growing importance, and James Watt realized that efficiency could be increased by using different cylinders for expansion and condensation of the steam. This drove his search for a linkage that could transform rotation of a crank into a linear slide, and resulted in his discovery of what is called Watt's linkage. This led to the study of linkages that could generate straight lines, even if only approximately; and inspired the mathematician J. J. Sylvester, who lectured on the Peaucellier linkage, which generates an exact straight line from a rotating crank.

Four bar chain

coupler crank follower frame A 4-bar linkage mechanism has a crank that rotates at a constant angular speed. The crank is connected to the coupler which is connected to the follower. The frame does not move. Notice that the crank rotates at a constant angular speed. The coupler provides a constant distance between the movable ends of the crank and the follower. coupler crank follower frame

Grasshof’s Theorem The motion characteristics of a-four-bar mechanism will depend on the ratio of the link length dimensions. A Grasshof’s linkage is a planar four-bar linkage with S + L < P + Q where S = length of the shortest link L = length of longest link P and Q are the lengths of the two remaining links.

1. Crank-Rocker : a Grashof linkage where the shortest link is the input link (crank). 2. Double-Rocker: a Grashof linkage where the shortest link is the floating link (coupler). 3. Rocker-Crank : a Grashof linkage where the shortest link is the output link (follower). 4. Crank-Crank : a Grashof linkage where the shortest link is the ground link (frame).

There are many possible variations in the design of a 4-bar linkage mechanism. Four examples are given in the diagrams below.

This mechanism is a crank-rocker This mechanism is a crank-rocker. Notice that the crank is the shortest link.

This mechanism is a crank-crank. This mechanism is a double rocker. Notice that the frame is the shortest link. This mechanism is a double rocker. Notice that the coupler is the shortest link.

Applications Coupled wheel of Locomotive Engine

Beam engine

Watt’s indicator mechanism

Other possible mechanism basis on four bar.

Animations

Thank you Guided By, Dinesh M Patel Prepared By, Darshan S Parmar(130990119028) Priyank M Patel(130990119037) Shivam S Patel(130990119038) Vimal M Patel(130990119041)