This paper deals with the problematic of the drive system of small-diameter knitting machines (hereinafter “knitting machines”). An alternative design of a new drive system is presented that addresses the effective working position of selected operating elements, i.e., a cylinder, a dial, and a roller cutter. The design is protected by patent No. 303578, and the authors of this paper also authored the patent. For the description and simulation of the drive system, mathematical models have been elaborated of the existing and new drive system, which include an additional design of a more suitable stroke for the movement of the cylinder. The output of the simulations are the courses of kinematic quantities, torque, and electric current, elucidating the benefits of the new drive system. Based on the structure of the new drive system, a test device has been designed and manufactured to verify functionality and reliability. The new drive system consumes less energy, simplifies the machine frame and reduces noise emissions. The obtained results can help in researching the issue of knitting machine frames, and in addition, the new system brings new technological possibilities for knitting.