Chapter Four: Vector Loops

  Chapter Four - Vector Loops

Learning to Love Loops!

        Have you ever woken up in the morning and wanted to draw a vector loop for a four-bar linkage?

        

       I haven't either, but we're going to do one today.

    Sometimes it is necessary to draw a vector loop for a four-bar linkage. Such a case is with a crank slider, where the rocker is not a physical link and must be imagined. Slider cranks are popular inversions of the four-bar and have real world applications with things such as pistons.

    

    This image depicts a as the crank, b as the coupler, c as the rocker, and d as the ground.

    The x and y components of this crank slider can be broken up into two separate equations, as follows:

            

                    → x component: a*cosθ2 - b*cosθ3 - c*cosθ4 - d = 0, where θ2  and θ4 will be known

                    → y component: a*sinθ2 - b*sinθ3 - c*sinθ4  = 0

    The x component of the equation can be rearranged to solve for d, and the y component can be rearranged to solve for θ3. Once these values are known, the x and y components of the slider can be known for any θ2  value of the crank. This is useful when trying to find the maximum or minimum displacement of the slider. Finding the maximum or minimum displacement of the slider is very important in piston applications - it would be disastrous to make a cylinder shaft for a piston that is shorter than the maximum displacement of the piston.