Variable impedance actuators: A review <s> Combinations of inherent compliance and damping <s> In order to study the roles of muscle mechanics and reflex feedback in stabilizing movement, experiments were conducted in which healthy human subjects performed targeted wrist movements under conditions where the damping of the wrist was reduced with a load having the property of negative viscosity. If the movement speed and negative viscosity were sufficiently high, the wrist oscillated for several hundred milliseconds about the final target position. Subjects increased the activation of both wrist flexor and extensor muscles to increase joint stiffness to damp the oscillations. With practice, both the tendency to oscillate and the level of muscle activation were reduced. A small bias torque in either direction, added to the negative viscosity, enhanced the oscillations as well as the amount of flexor and extensor muscle activation during the stabilization phase of fast movements. The tendency for the wrist to oscillate was also seen during slow movements where the oscillations were superimposed upon the voluntary movement. We suggest that this reduction in mechanical stability is primarily of reflex origin. As wrist stiffness increases, the natural frequency of the wrist also increases, which in turn produces an increase in the phase lag of the torque generated by the myotatic reflex with respect to wrist angular velocity, effectively reducing damping. The oscillation frequency was often close to a critical frequency for stability at which torque, due to the myotatic reflex, lagged angular velocity by 180° (6–7.5 Hz). Nevertheless, subjects were able to damp these oscillations, probably because the torque due to intrinsic muscle stiffness (in phase with position and hence lagging velocity by only 90°) dominated the torque contribution of the myotatic reflex. Increasing stiffness with declining oscillation amplitude may also have contributed significantly to damping. <s> BIB001 </s> Variable impedance actuators: A review <s> Combinations of inherent compliance and damping <s> A novel force/torque control actuator called series damper actuator (SDA) is proposed, modeled and analyzed. Compared to conventional force/torque control schemes and series elastic actuator (SEA), SDA has good output force/torque fidelity, low output impedance and large force/torque range. Furthermore, varying damping coefficient endows the SDA with more advantages and makes the system more versatile. An experimental SDA system is developed, in which a magnetorheological (MR) fluid damper is employed as the series damper. The experimental results show that SDA system is an effective force/torque control actuator. <s> BIB002 </s> Variable impedance actuators: A review <s> Combinations of inherent compliance and damping <s> We describe the design of an eddy current brake for use as programmable viscous damper for haptic interfaces. Unlike other types of programmable brakes, eddy current brakes can provide linear, programmable physical damping that can be modulated at high frequency. These properties makes them well suited as dissipative actuators for haptic interfaces. We overview the governing physical relationships, and describe design optimization for inertial constraints. A prototype haptic interface is described, and experimental results are shown that illustrate the improvement in stability when simulating a stiff wall that is made possible using programmable eddy current dampers. <s> BIB003 </s> Variable impedance actuators: A review <s> Combinations of inherent compliance and damping <s> Until now, design of variable physical impedance actuators (VIAs) has been limited mainly to realising variable stiffness while other components of impedance shaping, such as damping, are either fixed (e.g., with the addition of fixed passive dampers) or modulated with active feedback control schemes. In this work we introduce an actuator that is capable of simultaneous and independent physical damping and stiffness modulation. Using optimal control techniques, we explore how variable physical damping can be exploited in such an actuator in the context of rapid movement. Several numerical simulation results are presented, in addition to an experiment realised on variable impedance robotic hardware. <s> BIB004
Some devices combine a variable damping actuator with an elastic element. To give an overview of the different possibilities consider a system described by: 1) one motor with an output shaft, 2) one containment frame, 3) one elastic connection between the motor and the shaft, and 4) one source of damping action. Since the list of system topologies grows exponentially with the number of elements considered, we limit our analysis to systems composed of those four elements only. This gives rise to the four possible configurations shown in Fig. 12 . Note that the damping action, represented with a pure damper in Fig. 12 , could also be implemented with a hybrid visco-elastic element, this would imply slight modifications to equations 7-10. In this section we present an accurate analysis of these connection topologies and highlight benefits and drawbacks of each solution. The topology depicted in Fig. 12(a) shows a stiffness and a damper in parallel between the reference and the link. The link dynamics of this layout is described by where m represents the link inertia, d the damping, k the stiffness, q the link position, θ the reference position. This scheme has been considered in  . The scheme depicted in Fig. 12 (b) presents a stiffness between the reference and the link, and a damper between the link and the external frame. The link dynamics of this layout is described by This topology is featured, for example, in models of corresponding to a model of human limb impedance at a joint BIB001 . One drawback of system (b) is a b c d Figure 12 : The four possible layouts to add a damping action to a system coupling a motor with a load through an elastic connection: a) pure parallel, b) external parallel, c) serial spring first and d) serial damper first. The damping action can be introduced trough a pure damper, as shown in the figure, or with visco-elastic elements. More complex layouts are possible if a larger number of components is considered. that, during link motion, the damper resistance must be overcome. This can be done by realizing a variable damping mechanism that can be completely turned off. On the other side, this system has the advantage of allowing the designer to realize it as an add on which can be attached externally to another actuation unit. This has been done using the variable fluid damping device of Catalano et al.  , which is combined with the Qbot module  . Radulescu et al. BIB004 proposed the Maccepa-VD (Maccepa with Variable Damping) where the damper is a back-drivable motor/gearbox that exploits the DC motor damping effect. It is not the like in system (a), which has to be integrated into the device. Schemes in Fig. 12 (c) and (d) present a serial connection of a spring and a damper between the reference and the link. The link dynamics of these layouts are described by and mq + k(q − q m ) = 0 d(q m −θ) + k(q m − q) = 0 respectively. These two schemes are similar to those adopted in BIB003 and BIB002 and present the advantage of minimizing the amount of motor inertia reflected to the link. Nevertheless, they have the major disadvantage of requiring continuous rotation of the motor to apply a constant torque to the output. Some other differences arise between the four schemes, for instance, to achieve the behavior of a pure VSA, the damping factor should be null for layouts (a) and (b), while it should tend to infinity for layouts (c) and (d).