Chapter 3: Graphical Linkage Synthesis

Straight Line Linkages

Getting Handy with Hoeken!

    The Hoeken straight line linkage produces approximately straight motion along a curve. This motion can be optimized for straightness or for constant velocity. At the extremes of the two, some sacrifices have to be made. Overoptimized straightness and velocity comes at a limited range of motion that this straightness will be in - i.e., the motion will be straight for a smaller distance. This can be seen by using the table located in the textbook.

    The Maximum ΔCy% column of the table indicates how much Cy is allowed to change along the straight portion of the motion. 0.00001% indicates that Cy can only change in vertical position by that percent - making it the most constrictive option in the table. Δx in the table is the section of the curve that is straight. 

    Considering first a ΔCy of 0.00001% and a L2 length of 1 in, the Δx value would be 0.601 inches. For a ΔCy of 0.096% and an equal link length, the Δx value would be 4.181 inches. The 000001% value represents a considerable amount more than the 0.096% value but comes at a large price in terms of straightness. The same trade-offs happen with constant velocity (right side of the table) at an even larger amount. It is therefore important to consider straightness versus length of straightness when designing using Hoeken straight line linkages.

    Hoeken linkages are used in applications relating to the world of robotics. The robots use multiple legs to approximate straight line motion and constant velocity to create a stable walk. This can be seen the YouTube link below.

                                                            https://youtu.be/ctTK6aSjrgc