Graphical Synthesis for Limit Positions of a Four-Bar Mechanism Using the Triangle Inequality Concept

An innovative methodology is presented for a set of synthesis problems in which the mobility angle between limit positions of a side link of a four-bar mechanism is necessarily prescribed. The principles used in synthesis are derived from a graphical interpretation of the triangle inequality concept. The derived principles give valuable insight to the solution space by dividing it into two separate regions. One region yields only Grashofian mechanisms, and the other region yields only non-Grashofian mechanisms. This information gives the designer a method for generating all possible mechanisms which satisfy the limit position and mechanism type constraints. A major advantage of the graphical technique is that is uses simple geometric objects, and therefore it can be easily implemented on most CAD packages. Several examples are used to demonstrate the concepts.