We say that the Jacobian is full rank at a configuration theta if the rank is equal to the minimum of 6 and n. This means that the rank of the Jacobian can be no greater than the minimum of 6 and n. The Jacobian is a 6 by n matrix, where n is the number of joints. The twists and wrenches can be expressed in the space frame.

We’ve seen two major uses of Jacobian matrices: converting a set of joint velocities theta-dot to an end-effector twist V and converting an end-effector wrench F to a set of joint forces and torques tau.