The kinematic flexibility of articulated arms containing one degree of redundancy

The paper extends the notion of kinematic flexibility to redundant robots. The kinematic flexibility is defined as the (hyper)volume of the domain of the values of joint angles correspondent to the given combination of task coordinates. By the measure of kinematic flexibility it is possible to quantify redundancy. We can grade mechanisms with the same or different number of joints and mathematically determine which of them is more redundant or in which region of the workspace the mechanism can provide more freedom in programming and controlling tasks.