Manual wheelchairs, which are the basic means of transport for people with disabilities, are usually characterized by an inefficient adaptation to the physical capabilities of their users. For this reason, it is advisable to search for solutions that will allow us to change the parameters of the mechanical power generated by human muscles. For this purpose, mechanical gearing known from other solutions, for example, from bicycles, can be used. The paper describes the design methodology and a number of issues related to the construction of an innovative wheelchair prototype using a chain transmission in its drive system. This solution allows for the implementation of a variable ratio between the wheels and the pushrims. Thus, it effectively allows for matching the demand for driving torque to the movement conditions and the physical capabilities of its user. The use of such a system provides the basis for increasing the efficiency of the manual propulsion process. Initial studies show that changing the gear ratio allows for different speeds of the wheelchair wheel. In the tests conducted, the root mean square of this value varied from 15.2 RPM to 35.5 RPM, which resulted in a change in power from 15.8 W to 40.1 W. Of course, the values of rotational speed and torque show a cyclically changing character, which results from the intermittent nature of generating drive by the wheelchair user. The average peak values of rotational speed were 31.4 ± 1.7 RPM, 44.3 ± 3.4 RPM and 57.9 ± 3.4 RPM, while the torque was 12.1 ± 0.5 Nm, 12.4 ± 0.4 Nm and 14.1 ± 0.6 Nm for Gears 1, 4 and 6, respectively.