Position Analysis of a 4 Bar RRRR Grashofian Double Crank
Introduction

Position Analysis of  a Grashofian Double Crank RRRR Mechanism

Schematic diagram of 4 Bar RRRR Linkage
 

Schematic Diagram of a 4 Bar RRRR Linkage

 

The 4 bar RRRR mechanism is forms the basis of any study on mechanism. It is widely used in various forms because of the relative simplicity of design and manufacture as well as durability. Grashof's criteria is used to distinguish between 4 bar RRRR linkages depending on the rotatability of the individual links of a 4 bar mechanism. In brief, if l is the longest link, s the longest link and the other two links have length p and q then the following cases arise
  • l + s < p + q : Grashofian linkage
    • l + s < p + q , shortest link s is the ground link : Double Crank 
    • l + s < p + q , shortest link is the coupler : Double Rocker
    • l + s < p + q , shortest link is neither coupler nor ground : Crank Rocker
  • l + s > p + q : Non Grashofian Double Rocker

For a more detailed introduction to Grashof criteria see the animated guide that follows. You can either click on the animation itself to move from step to step as per your convenience. Alternatively you can use the controls at the bottom of the animation to see it at your own pace.

In a Double Crank both the input link (link 2) and the output link (link 4) can rotate through a full circle. The position analysis of a Double Crank  involves finding out the coupler curve (that is the curve traced by a point on the link 4, which is the coupler, or its extensions) and the relation between the input and output orientations, that is  the relation between theta 2 and theta 4. Since the input link rotates through a full circle it is possible to drive this mechanism using a simple continuous rotary drive, that is we may connect it directly to a simple motor. Likewise we can connect the output to a continuous rotary drive directly too. Thus we can use this mechanism to cyclically generate a varying pattern of  rotation by suitably choosing the link lengths and simply connecting the input link to a constant RPM motor. Alternately a constant torque motor at the input can produce a varying torque at the output, which also implies a varying mechanical advantage.