A surgical robotic system has a surgical robotic arm, and a programmed processor that determines a longest principal axis of a velocity ellipsoid for a first configuration of the arm, applies a maximum task space velocity (that is in the direction of the longest principal axis) to an inverse kinematics equation which computes a potential joint space velocity, computes a ratio of i) the potential joint space velocity and ii) a joint space velocity limit of the arm, and applies the ratio to an initial joint space velocity, to produce a regulated joint space velocity. Other aspects are also described and claimed.