This book is an introduction to the geometric theory used to design linkage systems that are components of machines ranging from vehicle suspensions to robot arms. The focus throughout is on graphical synthesis of linkages to control the movement of the legs for a walking machine. Increasingly complicated walking machines obtained from patent drawings, art and technology are used to motivate the theory.
Starting with legs formed by rotating cranks, we move to legs constructed from four bar linkages with specially shaped coupler curves. This leads to a search for coupler points that have near straight line trajectories, and motivates constructions for the inflection circle and cubic of stationary curvature. We also consider cognate linkages and those with symmetric coupler curves.
The use of an RR serial chain controlled by the coupler curve of a four-bar linkage is our introduction to six-bar linkages. Then skew pantographs that provide scaling and reorientation of a coupler curve for better walking movement, which yield eight-bar linkages. The legs designed by Theo Jensen and Amanda Gassaei are shown to implement four bar function generators that control the joint movement of an RR chain. This leads to graphical two and three position synthesis of four-bar function generators, which are applied to the design of legs with two and three specified configurations.
We conclude with a discussion of the duty factor and support pattern needed to assemble two, four and six legged walking machines. The result is walkers that provide level straight line movement with one actuator. The challenge of designing steering and suspension systems for these walkers is left for the future.
