Although numerous researches on s-curve motion profiles have been carried out, up to date, no systematic investigation on the general model of polynomial s-curve motion profiles is considered. In this paper, the model of polynomial s-curve motion profiles is generalized in a recursive form. Based on that, a general algorithm to design s-curve trajectory with time-optimal consideration is proposed. In addition, a special strategy for planning s-curve motion profiles using a trigonometric model is also presented. The algorithms are implemented on a linear motor system. Experimental results show the effectiveness and promising application ability of the algorithms in s-curve motion profiling.