Synthesis of planar five-bar pantograph configurations by a geometric method

We present a geometric method for structural synthesis of planar five-bar pantograph configurations. Based on the concept of similarly varying triangles, the geometric conditions for a five-bar linkage to be a pantograph are derived according to a complex number approach. Under these conditions, a geometric procedure is proposed to synthesize all five-bar pantograph configurations with four or three similarity points systematically. In total 13 configurations with four similarity points and 23 configurations with three similarity points are obtained. The results of this work provide a complete atlas of pantograph configurations superior to existing ones.