Constant torque compliant mechanisms produce an output torque that does not change in a large range of input rotation. They have wide applications in aerospace, automobile, timing, gardening, medical, and healthcare devices. Unlike constant force compliant mechanisms, the synthesis of constant torque compliant mechanisms has not been extensively investigated yet. In this paper, a method is presented for synthesizing constant torque compliant mechanisms that have coaxial input rotation and output torque. The same shaft is employed for both input rotation and output torque. A synthesized constant torque compliant mechanism is modeled as a set of variable width spline curves within an annular design domain formed between a rotation shaft and a fixed ring. Interpolation circles are used to define variable width spline curves. The synthesis of constant torque compliant mechanisms is systematized as optimizing the control parameters of the interpolation circles of the variable width spline curves. The presented method is demonstrated by the synthesis of constant torque compliant mechanisms that have different number of variable width spline curves in this paper.