The Roles of Shape and Motion in Dynamic Manipulation: the Butterfly Example

We are studying a juggler’s skill called the “butterfly.” Startingwith a ball resting on the palm of his/her open hand, a skilled juggler can accelerate and shape his/her hand so that the ball rolls up the fingers, over the top, and back down to the back of the hand. This paper describes a robotic implementationof the butterfly. The hand’sshape and motion combine to effect the rolling motion of the ball, and we find that the shape and motion parameters enter the dynamic equations in a similar way. We define parameterized spaces of hand shapes and motions, and using a simulation based on the rollingequations, we identify shape and motion solutions that roll the ball from one side of the hand to the other. We describe an implementationof the butterfly on our planar dynamic manipulationtestbed FLATLAND. This example is our first step toward exploring the roles of shape and motion in dynamic manipulation.