Kinematically redundant manipulators admit an infinite number of inverse kinematic solutions and hence the optimization of different performance measures corresponding to various task requirements must be considered. Joint accelerations of these mechanisms are usually computed by optimizing various criteria defined using the two-norm of acceleration vectors in the joint space. However, in formulating the optimization measures for computing the inverse kinematics of redundant arms, this paper investigates the use of the infinity norm of joint acceleration (INAM) (also known as the minimum-effort solution). The infinity norm of a vector is its maximum absolute value component and hence its minimization implies the determination of a minimum-effort solution as opposed to the minimum-energy criterion associated with the two-norm. Moreover, the new scheme reformulates the task as the online solution to a quadratic programming problem and incorporates three levels of joint physical limits, thus keeping the acceleration within a given range and avoiding the torque-instability problem. In addition, since the new scheme adopts the LVI-based primal–dual neural network, it does not entail any matrix inversion or matrix–matrix multiplication, which was embodied in other's researches with expensive O(n3) operations. This new proposed QP-based dynamic system scheme is simulated based on the PUMA560 robot arm.