LAUSR

The wrench model is a necessity to implement the ironless permanent magnet planar motor. In order to guarantee its feasibility, the existing research studies always conduct the coil shape simplification (CSS) and the wrench vector component simplification (WVCS) during the modeling process. This paper focuses on the necessity of two kinds of simplifications and theoretically analyzes their performance affection from the model accuracy aspect and the calculation speed aspect. First, based on the analytical expression of the unified wrench model which denotes a more general case than the analytical model proposed by previous researchers and could describe the wrench model, no matter what kind of simplification is conducted, we prove that the CSS must cause accuracy deterioration. However, the model with more WVCs will certainly be more accurate only in the case that the CSS is not conducted. In terms of calculation speed, the influence of the WVCS is much more than that caused by a concise wrench coefficient matrix which may result from the CSS. Then, we give a special case to graphically illustrate these discussions. Finally, the general conclusion goes that the wrench model including no CSS and appropriate WVCS depending on demands of real-time calculation has the better comprehensive performance from the model accuracy and calculation speed aspect. This conclusion brings convenience to the relevant research studies that the time-consuming verification process about model accuracy can be omitted.