## 1 Introduction
The earliest synchronous planar motor was proposed by [PERSON] [17], in which there are four groups of linear synchronous units. Each unit can be seen as a slotless linear motor which is composed of a 1-D Halbach magnet array and three-phase windings. In 2002, [PERSON] et al. [18] proposed a new synchronous planar motor, which is composed of a 2-D permanent-magnet array and four 1-D coil arrays. The performances of several 2-D permanent-magnet arrays are compared with each other. In 2007, a novel moving-magnet synchronous planar motor was proposed by [PERSON] et al. [19]. The motor consists of a 2-D permanent-magnet array and a 2-D coil array. In the 2-D coil array, there are two groups of track-shape coils which are orthogonal and arranged in turn. Obviously, this moving-magnet topology has no moving cables and the heat from a coil array can be easily reduced by adopting cooling solutions. The above three types of motors are long-stroke planar motors, in which the moving range is usually hundreds of millimeters. However, high-accuracy performance at a millimeter level is often required in many applications. In this case, the Lorentz-force-driven planar motor [20; 21; 22] is the best solution due to the inherent features of unlimited resolution, high linearity, no force-ripple, etc. Actually, it is more often the case that high accuracy and long stroke are both required in some systems [23; 24]. Therefore, the coarse-fine scheme is usually adopted, in which the Lorentz-force-driven planar motor is located on top of the system in order to achieve the precision compensation. The Lorentz-force-driven planar motor needs to be well designed and optimized to simplify the system-level structure and improve the integral dynamic performance, because it lies on the top of the positioning system. Compared with the long-stroke motors at the bottom, the optimization work for the short-stroke motors can do more contributions to the improvement of system performance. At present, the finite element method is usually used in most of the studies in the established literature concerning the design and optimization for planar motors. Obviously, it is a time-consuming method to analyze the planar motors that cannot be completely described by a 2-D finite element model. In this study, we describe a short-stroke Lorentz-force-driven planar motor. The analytical model containing the air-gap magnetic field, inductance and force expression is built. Based on the model, the main design parameters are determined and the specific influences of the main parameters on motor performances are analyzed. Three important indexes (i.e., the force, force density, and acceleration) are optimized and the reasonable values for the dimensional parameters are concluded. Compared with [1], the main dimensions' equation is transformed to the force equation in this paper, which is more important for motor optimization. Additionally, the analytical expressions for the force density and acceleration are derived, and the corresponding variation curves are given, which are very important references for this type of motor. Finally, based on the optimization results, reasonable ranges for the main parameters are given, which can balance the force, the force density, and the acceleration for the proposed planar motor.