Although it sounds correct and could pass without a glance, if you examine the logic of the sentences, they mean something slightly different.
An on-screen keyboard allows people with mobility impairments to type data using a joystick or a pointing device.
The first sentence states that people with mobility impairments use the joystick and pointing device in order to operate the on-screen keyboard.
An on-screen keyboard allows people with mobility impairments to type data by using a joystick or a pointing device.
By using a joystick or a pointing device, an on-screen keyboard allows people with mobility impairments to type data.
The second sentence states that the on-screen keyboard is the one that uses the joystick or pointing device to allow impaired people to type data.
The difference: In one of them, the people use the joystick in order to control the machine.
In the other, the machine uses a joystick so that people can control it. Both of them are true in this case, but they aren't the same.