Variable impedance actuators: A review <s> Lever length <s> Variable stiffness actuators are a particular class of actuators that is characterized by the property that the apparent output stiffness can be changed independent of the output position. To achieve this, variable stiffness actuators consist of a number of elastic elements and a number of actuated degrees of freedom, which determine how the elastic elements are perceived at the actuator output. Changing the apparent output stiffness is useful for a broad range of applications, which explains the increasing research interest in this class of actuators. In this paper, a generic, port-based model for variable stiffness actuators is presented, with which a wide variety of designs can be modeled and analyzed. From the analysis of the model, it is possible to derive kinematic properties that variable stiffness actuator designs should satisfy in order to be energy efficient. More specifically, the kinematics should be such that the apparent output stiffness can be varied without changing the potential energy that is stored in the internal elastic elements. A concept design of an energy-efficient variable stiffness actuator is presented and implemented. Simulations of the model and experiments on the realized prototype validate the design principle. <s> BIB001 </s> Variable impedance actuators: A review <s> Lever length <s> The Actuator with Adjustable Stiffness (AwAS) is an actuator which can independently control equilibrium position and stiffness by two motors. The first motor controls the equilibrium position while the second motor regulates the compliance. This paper describes the design and development of AwAS-II which is an improved version of the original realization. AwAS tuned the stiffness by controlling the location of the springs and adjusting its arm, length. Instead AwAS-II regulates the compliance by implementing a force amplifier based on a lever mechanism on which a pivot point can adjust the force amplification ratio from zero to infinitive. As in the first implementation, the actuator which is responsible for adjusting the stiffness in AwAS II is not working against the spring forces. Its displacement is perpendicular to the force generated by springs which makes changing the stiffness energetically efficient. As the force amplification ratio can theoretically change from zero to infinitive consequently the level of stiffness can tune from very soft to completely rigid. Because this range does not depends on the spring's rate and length of the lever, thus soft springs and small lever can be used which result in a lighter and more compact setup. Furthermore as the lever arm is shorter the time required for the stiffness regulation is smaller. <s> BIB002 </s> Variable impedance actuators: A review <s> Lever length <s> For tasks that require robot-environment interaction, stiffness control is important to ensure stable contact motion and collision safety. The variable stiffness approach has been used to address this type of control. We propose a hybrid variable stiffness actuator (HVSA), which is a variable stiffness unit design. The proposed HVSA is composed of a hybrid control module based on an adjustable moment-arm mechanism, and a drive module with two motors. By controlling the relative motion of gears in the hybrid control module, position and stiffness of a joint can be simultaneously controlled. The HVSA provides a wide range of joint stiffness due to the nonlinearity provided by the adjustable moment arm. Furthermore, the rigid mode, which behaves as a conventional stiff joint, can be implemented to improve positioning accuracy when a robot handles a heavy object. In this paper, the mechanical design features and related analysis are explained. We show that the HVSA can provide a wide range of stiffness and rapid responses according to changes in the stiffness of a joint under varying loads by experiments. The effectiveness of the rigid mode is verified by some experiments on position tracking under high-load conditions. <s> BIB003 </s> Variable impedance actuators: A review <s> Lever length <s> In this paper, the vsaUT-II, a novel rotational variable stiffness actuator, is presented. As the other designs in this class of actuation systems, the vsaUT-II is characterized by the property that the output stiffness can be changed independently of the output position. It consists of two internal elastic elements and two internal actuated degrees of freedom. The mechanical design of the vsaUT-II is such that the apparent output stiffness can be varied by changing the transmission ratio between the elastic elements and the output. This kinematic structure guarantees that the output stiffness can be changed without changing the potential energy stored internally in the elastic elements. This property is validated in simulations with the port-based model of the system and in experiments, through a proper control law design, on the prototype. <s> BIB004 </s> Variable impedance actuators: A review <s> Lever length <s> In this paper, we present the mechanical design of the mVSA-UT, a miniaturized variable stiffness actuator. The apparent output stiffness of this innovative actuation system can be changed independently of the output position by varying the transmission ratio between the internal mechanical springs and the actuator output. The output stiffness can be tuned from zero to almost infinite by moving a pivot point along a lever arm. The mVSA-UT is actuated by means of two motors, connected in a differential configuration, which both work together to change the output stiffness and the output position. The output shaft can perform unbounded and continuous rotation. The design ensures high output torque capability, light weight and compact size to realize a multiple purpose actuation unit for a great variety of robotic and biomechatronic applications. <s> BIB005
A lever has three principal points: the pivot; the spring attachment point, i.e. where the springs are located; the force point. By changing the position of one of these parameters a variable stiffness independent from the equilibrium position is created (Fig. 7) . Using the lever method produces energetically efficient stiffness adjustment since the displacement needed to change the stiffness is perpendicular to the force generated by the springs, however, most of the time the passive joint range is limited compared to other designs. The vsaUT BIB001 is based on a lever arm of variable effective length, connecting the internal (zero free length) spring to the output. This essentially moves the point of application of the output force along the lever. The zero free length spring is generated by a pair of extension springs in antagonistic setup, acting on the rotation axis of the lever arm. The working principle of the vsaUT BIB001 is based on a lever arm of variable effective length, which connects the internal (zero free length) spring to the output, and it is realized by moving the point of application of the output force on the lever. The zero free length spring is practically realized by a pair of extension springs in antagonistic setup, acting on the rotation axis of the lever arm. In AwAS  the force and pivot point are fixed and to change the stiffness the spring point is changed (Fig. 7a) . The range of stiffness depends on the stiffness of the springs and length of the lever. This method is also used in BIB003 . In AwAS-II BIB002 force and spring points remain constant with the pivot point now changing (Fig. 7c) . In this mechanism the stiffness is zero when the pivot reaches the spring point increasing to infinite when the pivot and force point coincide. This very high range does not depend on the stiffness of the springs and lever length, hence short levers and soft springs can be used giving a lighter, more compact setup compared to the AwAS. CompAct © -VSA is an improved version of AwAS II using a cam shaped lever arm with a variable pivot axis actuated by a rack and pinion transmission system  . The idea of changing the pivot point is also used in vsaUT-2 BIB004 . The stiffness change mechanism uses a ring gear, with pitch diameter d, and a pivot gear with pitch diameter d/2, to which the pivot point is connected. Due to the precise ratio between the pitch diameters, the pivot point moves in a straight line with respect to the ring gear when the pivot gear runs in the ring gear. Since the pivot moves in a straight line, no guides are needed, ensureing low friction when moving the pivot point. This concept is used in the mVSA-UT BIB005 , which is actuated by differentially connected two motors, responsible for changing both the output stiffness and position. More specifically, in its realization, the output stiffness can vary from zero to almost infinite by moving the pivot point along the lever arm and the output shaft can perform unbounded and continuous rotations.