The purpose of a mechanism is transmit motion and force (or torque) from one location to another. The challenge when designing a good mechanism deals with the relationship between position and force (which always hold and become a constraint on the design) and the fact the equations are inherently nonlinear (although a mechanism can be approximately linear over a short travel range). The relationship between position, velocity and force is through the kinematic equations and mechanical advantage relationships. In any mechanism design, there will always be some trail and error (or experimentation) that must occur.

Design methods for four bar linkages encompass generic trial and error plus standard textbook methods. Design solutions using any methodology are not guaranteed, so it is possible to pose a four bar linkage problem that is not kinematically feasible. Therefore, flexibility and creativity is important in linkage design. Intuition and insight are also helpful. Intuition and insight can be gained by understanding the equations governing four bar linkages and by reviewing the design examples provided here. Practice and experience is also helpful for developing insight.

Design methods for four bar linkages fall 5 general categories:

Mathematical

Trial & Error

Function Generation

Motion Synthesis

Path Synthesis

Within each category, there are various approaches to design that can be taken. In some categories, extensive methods are developed in mechanism textbooks. Some methods are mathematical based and some are graphical.

The reason for presenting all methods is to provide a good overview of the approaches and how they work. When designing a four bar linkage mechanism, any combination of these methods or other ad hoc method that an engineer chooses to use is acceptable for designing a linkage to meet the requirements. Requirement verification should always be completed prior to finalizing a design.

__Mathematical
Approach__

A purely mathematical approach is good for analysis but does not account for geometric constraints so a 3D layout should be part of a mathematical based design process. The mathematical approach uses the equations from Four Bar Linkage – Equations module. The iteration procedure using the position and velocity equations is used to determine the velocity ratios and thus the gearing ratio over the range of movement. An example is provided in Four Bar Linkage – Mathematical Design.

__Trial
and Error__

Trial and error relies on a basic understanding of constraints involved in four bar linkage operation and is the most common method used in industry. Usually in aerospace, many parameters are defined (such as ground points on structure) which simplifies the trial and error process. Knowing which points are fixed in a mechanism (such as ground points) and understanding how motion is constrained (such as movement constrained to an arc), trial and error can be quite fast. The best way to demonstrate the trial and error process is through an example. An example is provided in Four Bar Linkage – Trial and Error Design.

__Function
Generation__

Function
generation is a methodology to design a four bar linkage such that
the relationship between input and output motion follows a given
mathematical relationship. For example, if the input motion
(rotation) is represented by x and the output motion (rotation) is
represented by y, the function generation provides a method to design
a linkage such that y = x^{1.5} holds over a range of input
link rotation. Both mathematical and graphical approaches have been
developed to accomplish function generation. An example of a
mathematical approach (Freudenstein’s Method) is provided in Four
Bar Linkage – Function Generation. Graphical methods also
exist. The most common graphical method is the Overlay Method. An
item of note with function generation is that since the method
applies to position relationships and not velocity relationship, the
method does not directly allow a person to design for both travel and
gearing ratio.

__Motion
Synthesis__

Motion synthesis address the problem of designing a four bar mechanism to place a body in desired locations during rotation of the linkage. The body is the coupler component of the four bar linkage. Three desired positions of the body are required to design the linkage. These locations become the inputs. Two basic design methods exist; both are graphical methods. The first method is to select attach points for the linkage on the body (coupler) and then determine the location of the ground points. The second method is to select locations for the ground points and then determine the location of the input link and output link attach points on the body (coupler). Examples of these methods are provided in Four Bar Linkage – Motion Synthesis Ground Points Fixed and Four Bar Linkage – Motion Synthesis Ground Points Variable.

__Path
Synthesis __

Path synthesis is a four bar linkage design method to design a linkage such that a point on the coupler passes through selected points. At least three points must be provided. The method uses kinematic inversion to design the linkage. Inputs to this design methodology are the three coupler points and the location of the ground points. The output is the definition for link 1 and link 3 as well as the attach points on the coupler. An example of path synthesis is provided in Four Bar Linkage – Path Synthesis.