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This study investigates the concept, analysis, and design of the Permanent Magnet (PM) Trans-Rotary Magnetic Gear (TROMAG). The device converts linear motion to rotation and vice-versa through the magnetic field, and does the gearing action at the same time. It can convert the low speed high force linear motion of a translator to the low torque high speed rotation of a rotor; a promising capability for wave energy applications in particular. The structure of the TROMAG is presented, along with results of three-dimensional (3D) Finite Element Analysis (FEA), as well as the basic tenets of continuous force transmission in orthogonal directions by the elementary magnetic arrays. Moreover, a simple analytical method is set forth for calculating the force of the device. The method is based on the replacement of a PM by an equivalent current carrying coil and the electromagnetic image method theory. In addition, design and scaling of the TROMAG is discussed and the impact of several design parameters on the performance of the TROMAG is investigated through an accurate analytical model. Finally, transient performance of the TROMAG is discussed.