Modeling linkages is an essential part of designing dynamic systems. To design these mechanical systems successfully, it is essential to be able to calculate the position and velocity of any point on a linkage at any given time to better understand the linkage’s range of motion and speed. The primary linkages include the threebar slider crank, the slider crank, the fourbar, the inverted slider crank, the geared fivebar, and the sixbar linkage. The primary method of analyzing the linkages is first to derive a vector loop equation that represents the linkage, next to write those vectors in terms of the known lengths and unit vectors, and finally to solve. To find the velocity, simply take the derivative of that equation. Using matrix algebra, calculate the solution of the equation relating the known values to the missing angular and linear velocities. Shown below are the results of the MATLAB code I developed to solve the equations specified above for the given range of motion of the crank in the linkages.
