Design and Optimization of Planar Leg Mechanisms Featuring Symmetrical Foot-Point Paths

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Design and optimization of planar leg mechanisms featuring symmetrical foot-point paths are presented in this study. These leg mechanisms are designed in such a way that a corresponding walking machine has the flexibility required for walking on a rough terrain, while it can achieve fast locomotion, is easy to control, and requires minimal actuation for walking on a flat ground. In addition, such leg mechanisms are compact in size with respect to a specified horizontal stride.

Based on a set of functional requirements, the concept generation of a set of leg mechanisms is accomplished via a systematic methodology. By temporarily excluding the degree-of-freedom (DOF) associated with the up-and-down motion of the leg, and based on a set of evaluation criteria, six admissible one-DOF planar four-, six-, and eight-bar leg mechanisms are found to have the desirable features to be used as a leg mechanism.

It is argued that a symmetrical foot-point path can be advantageous in reducing the maximum driving torque and making the motion control of the leg easier. While the four- and eight-bar compound mechanisms have been studied, a new class of six-bar linkages with an embedded (skew-) pantograph featuring a symmetrical foot-point path is introduced. Construction and design limitations for six-bar mechanisms are explored. The guidelines to prevent double point(s) are derived and the conditions to select between the propelling and non-propelling portions of the path are established.

For the dimensional synthesis, the admissible mechanisms with and without an adjustable pivot are investigated. For those mechanisms with an adjustable pivot, one DOF is used for normal walking to provide an ovoid path which emulated that of humans, while the other (the motion of the adjustable pivot) is used only when necessary to walk over obstacles. For those mechanisms without an adjustable pivot, the sole DOF provides a large D- shaped path, with which the leg mechanisms are capable of performing the up-and-down as well as the back-and-forth motions, To exploit these to the fullest, a multi-objective optimization-based design problem formulation is developed to minimize the following three design objectives: (i) peak crank torque, (ii) maximum actuating force, and (iii) leg size. Results from the optimization model show that an eight-bar compound mechanism with an adjustable pivot and a six-bar mechanism without an adjustable pivot are the two best leg designs among those studied here.

Finally, further reduction of the actuating force and crank torque is successfully demonstrated by placing tension spring elements onto an already optimized eight-bar leg mechanism.