2-DOF Small-Size Piezoelectric Locomotion Platform with the Unlimited Motion Range

This paper presents numerical and experimental investigations of a small size piezoelectric locomotion platform that provides unlimited planar motion. The platform consists of three piezoelectric bimorph plates attached to the equilateral triangle-shaped structure by an angle of 60 degrees. Alumina spheres are glued at the bottom of each plate and are used as a contacting element. The planar motion of the platform is generated via excitation of the first bending mode of the corresponding plate using a single harmonic signal while the remaining plates operate as passive supports. The direction of the platform motion controlled by switching electric signal between piezoelectric plates. A numerical investigation of the 2-DOF platform was performed, and it was found out that the operation frequency of the bimorph plates is 23.67 kHz, while harmonic response analysis showed that the maximum displacement amplitude of the contact point reached 563.6 µm in the vertical direction while an excitation signal of 210 Vp-p is applied. Prototype of the 2-DOF piezoelectric platform was made, and an experimental study was performed. The maximum linear velocity of 44.45 mm/s was obtained when preload force and voltage of 0.546 N and 210 Vp-p were applied, respectively.

Instantaneous center/axis of rotation for planar and three-dimensional motion

This article discusses a direct analytical method for calculating the instantaneous center of rotation and the instantaneous axis of rotation for the two-dimensional and three-dimensional motion, respectively, of rigid bodies. In the case of planar motion, this method produces a closed-form expression for the instantaneous center of rotation based on a single point located on the rigid body. It can also be used to derive closed-form expressions for the body and space centrodes. For three-dimensional, rigid body motion, an extension of the technique used for planar motion locates a point on the instantaneous axis of rotation, which is parallel to the body angular velocity vector. In addition, methods are demonstrated that can be used to map the body and space cones for general rigid body motion, and locate the fixed point for the body.