Position Analysis

The position analysis for this mechanism can be broken down into two individual calculations, one for each input. The first analysis is on the 3-bar mechanism that comprises links 1, 2 and 3, where the value h₁ is the input to the system. We have a vector loop of the form

with unknowns θ₂ and θ₃. The solution to this loop is non-linear in its unknown variables, and as such θ₂ and θ₃ are solved for numerically using the two equations derived from the equation's real and imaginary parts:

The solution to these equations over the range of motion of h1(discussed in the next section) is as shown below:

Once this part of the analysis has been completed, the next portion of the position analysis can be carried out, which is a 4-bar mechanism with one sliding joint with variable h₂ as the input. The vector loop for this mechanism is:

with unknowns θ₅and θ₆. Once again due to its non-linearity, we pass the real and imaginary parts of the equation to MATLAB’s numeric solver vpasolve in order to find the unknowns. These component equations are:

Once all of the angles have been solved for, the locations of all of the points on the mechanism can be solved for by simply following the vector trails from the origin to that point. Since the mechanism is symmetric, all of the link positions and angles for the rest of the mechanism can be found by simply mirroring the known quantities about the line FE.

Setting the value of h₁at a constant 1 meter, and varying the value of h₂through its acceptable range, we get the following