Introduction: 4 Bar Linkage

A four-bar linkage is a fundamental kinematic chain used in many different systems both artificial and natural. This kinematic chain is found in nature in many animal skeletal structures, including the human knee [32] [33]. Four bar linkages are also used in mountain bike rear suspensions, and are the basis of many other suspensions such as the double wishbone [34] [35].

There are 4 configurations for this assembly, each of which will teach a different lesson to the user.
  1. Rocker-Rocker
  2. Rocker-Crank
  3. Crank-Rocker
  4. Crank-Crank
The Lesson Plan for the 4 bar linkage is attached to this page for the Instructors who wish to teach students about this device.

Kinematics Associated with this Device:
  1. Bar Linkages: In engineering there is a standard classification of four-bar linkages called the Grashof condition. A four-bar linkage satisfies the Grashof condition when Equation 4 is shown below;
    s l < p q (4)
Where s, l, p, and q, all denote lengths of one of the links; in particular s is the shortest link and l is longest link. Grashof four-bar linkages can be in one of four states. Each state is identified by the action of the input and driven links with the other two links consisting of a floating link and the grounded link. The first state is Crank-Crank in which the input and driven links can freely rotate completely around their pivot on the ground link. The second and third states are Crank-Rocker and Rocker-Crank, respectively, which are the opposite of one another. In Crank-Rocker the input link is able to rotate freely around its pivot on the ground link, while the driven link is only able to rock back and forth about its pivot on the ground link. The fourth state is Rocker-Rocker in which both the input and driven links are only able to rock back and forth about their respective pivots on the ground link. Figure 44 shows the different states with labeled linkages [35].
Four-bar linkages can also exist in states that do not meet the Grashof Condition, which are considered non-Grashof. Non-Grashof linkages are Rocker-Rocker when Equation 5 is true.
s l > p q (5)
Non-Grashof linkages are also possible when the sum of the lengths of the shortest and longest links is equal to the sum of the other two links, p and q. When this is true, the four-bar linkage can be found in any of the four Grashof states but will have a point of rotation in which all pivots will be collinear, which is referred to as the change point. A special case of this type of linkage is the parallel bar linkage [35] [36].

The different components of the device are provided in the BOM table displayed

Post Processing note: If you are printing with an FDM printer you should expect small ridges on parts where the extruder last touches the piece. Carefully inspect each piece after they are printed for these small imperfections as they will hinder the operation of your device.

[32] M. M. Wachowski, T. A. Walde, P. Balcarek, J. P. Schüttrumpf, S. Frosch, C. Stauffenberg, K.-H. Frosch, C. Fiedler, J. Fanghänel, D. Kubein-Meesenburg and H. Nägerl, "Total Knee Replacement with Naturl Rollback," Annals of Anatomy - Anatomischer Anzeiger, vol. 194, no. 2, pp. 195-199, 2012.
[33] M. Muller, "A Novel Classification of Planar Four-Bar Linkages and its Application to the Mechanical Analysis of Animal Systems," Philosophical Transactions: Biological Sciences, vol. 351, no. 1340, pp. 689-720, 1996.
[34] P. '. Hayes, S. Young and Doddy, "Buyer's Guide to Mountain Bike Suspension, Part 2," BikeRadar, 2010. [Online]. Available: [Accessed 2 October 2013].
[35] Wikipedia Contributors, "Four-bar Linkage," Wikipedia, The Free Encyclopedia, 5 September 2013. [Online]. Available: [Accessed 2 October 2013].
[36] E. Söylemez, Mechanisms, Ankara: METU Publication #64, 1999.

Step 1: Print 4 Bar Linkage Parts

Download the 13 .stl files and upload them to your 3D printer's system. The quality of each part will increase depending on the orientation of the part on the print tray. Print each respective part based on the orientations shown in the images provided.

Step 2: Post Process Individual Parts

Based on the brand and quality of your 3D printer, the tolerances of your parts will vary so your parts may not need any refinements, or they may need a lot. The steps we have provided are the techniques we found were useful for making the device run as smoothly as possible. The following tools were used to refine the parts; file (varying sizes), fine sandpaper, Dental picks.

For 4 Bar Linkage:
Ensure to bore/file out any thru holes so that the bars turn around the pivot axles with ease, but at the same time will allow the shape to remain in a polygon shape. Sand down the pivot axles as well.

Step 3: Assembling the Device

Crank-Crank Config.

  1. Insert the Crank-Crank adapter into the base
  2. Insert 4 bar arrow pin into the Crank-Crank adapter
  3. Insert the 4" linkage over the Crank-Crank adapter
  4. Insert the 2" linkage over the Crank-Crank adapter
  5. Insert 4 bar Long arrow pin into 2" Linkage
  6. Insert the 4 bar pivot axle into the 2" linkage
  7. Insert the 6" linkage over the 4 bar pivot axle
  8. Insert the 4 bar short arrow pin into the 4 bar pivot axle
  9. Place the 7" linkage so that it fits concentrically with the 4" and 6" linkage bars
  10. Insert the 4 bar pivot axle into the thru holes of the 7" and 6" linkage bars
  11. Insert the 4 bar short arrow pin into the pivot axle
  12. Insert the 4 bar input handle into the 7" and 4" linkage bars
  13. Insert the 4 bar long arrow pin into 4" linkage bar and input handle square thru hole
(All of the following configurations are taken from the perspective view of the base facing the text "four bar linkage.")
Crank-Rocker Config.
Note that the base linkage for this configuration is the 6" linkage bar, the leftmost bar is the 2" linkage bar the rightmost is the 4" linkage bar.

Rocker-Crank Config.
Note that the base linkage for this configuration is the 6" linkage bar, the leftmost bar is the 4" linkage bar, the rightmost is the 2" linkage bar.

Rocker-Rocker Config.
Note that the base linkage for this configuration is the 7" linkage bar, the leftmost bar is the 4" linkage bar, the rightmost is the 6" linkage bar.