I designed a robot arm that simulates the human elbow-forearm structure. The model consists of a one-axis upper arm part and a two-axis forearm part, connected by an elbow joint. With this model, I attempted to create a structure that can flex and extend at the joint and simultaneously rotate at the distal end of the forearm.
Geodesic curves on the cone were used for the two axes of the forearm part. Mathematically it is generally known that
· When a cone rolls on a plane, the conic vertex does not move [theorem 1], and
· When a cone rolls on a plane, the geodesic curve on the cone moves on a straight line on a plane [theorem 2].
With these theorems, I produced two movement models.
Model I: When two cones and the geodesic curves on the cones roll on the front and reverse sides of one plane, they always touch during motion on a straight line on the plane.
Model II: This is the movement model produced by adding a straight line that connects two conic vertexes to model I. Two geodesic curves on the cone can turn around the straight line.
It was shown that movement model II was a structure for which rotation at the distal end of the forearm part was possible simultaneously with flexion and extension at the elbow joint part. Movement model II was redefined from the geometric movement conditions near the point of contact of the two geodesic curves on the cone. Further modification of these geometric movement conditions resulted in a new model with more natural movement of a human elbow-forearm structure.