**1. Introduction**

The gait is severely affected by lower-limb amputation and neuromotor diseases and to compensate the lost limb or impaired legs additional movements are required [1]. Walking and other daily activities, such as going up and down stairs, getting up and sitting down, can be severely impaired, reducing the mobility of the patient [2]. Over the years, researchers seek to develop suitable actuators for assistive lower-limb devices such as prosthesis and exoskeletons [3, 4]. In general, this kind of actuators can be divided into three major groups: passive, semi-active, and active [5, 6]. Passive devices do not require a power source for operation, they are designed for each type of application and do not allow performance adjustments [6]. Semi-active devices only dissipate energy through controllable dampers [7]. Active-type devices, on the other hand, are capable of supplying and dissipating energy in a controlled way [6, 8, 9]. Despite the disadvantages of semi-active and passive prostheses, the number of active prostheses is still small and only the Power Knee™ (PK, Ossur, Iceland) is available on the market. In addition, exoskeleton knee actuators still need to be improved to properly reproduce the knee gait kinematics for low energy consumption. Filho et al. [10], Garcia et al. [11], and Martinez-Villalpando and Herr [6] propose the use of linear actuators with a serial elastic element (SEA) between the femur and the tibia. This configuration has characteristics such as impact tolerance, low mechanical output impedance and passive storage of mechanical energy [12, 13]. However, they are heavy devices with high energy consumption, making it difficult to be used in prostheses or exoskeletons [9, 14].

On the other hand, magneto-rheological fluids (MR) are colloidal solutions composed by up to 50% of their volume of magnetically polarized micro particles mixed with an inert oil, usually mineral-based or silicone-based [15]. When the fluid is subjected to an external magnetic field, its particles begin to form columnar structures parallel to the magnetic flux lines; this behavior changes the rheological properties of the fluid, such as yield stress and others, in a reversible and proportional way to the induced magnetic field [16]; the response time is in order of milliseconds [17]. Due to these characteristics, MR fluids are used to develop devices for many applications in engineering and industry: vehicle suspensions [18], clutches [19], brakes [20], structural vibration damping [21], intelligent prosthesis [5, 22–24] and others. MR devices usually present low energy consumption and high torque-to-weight ratio [25, 26], which is important to increase the energy efficiency and reduce the weight of prostheses and exoskeletons' actuators [27].

Although the advances in actuators technology, the active actuators used in robotic devices are still heavy and bulky [28], and the passive and semi-active ones cannot properly reproduce the movement of a healthy knee. To address the shortcomings of the knee actuators, we developed the Active Magneto-Rheological Knee (AMRK) [29, 30]. The actuator employs a motor-unit (MU), composed by an EC 60 flat motor (Maxon Motors, Switzerland), harmonic drive CSG-14-100-2a (Harmonic Drive AG, Germany) and MR clutch, that works in parallel to a MR Brake. With this configuration the actuator has multifunctional working conditions and can reproduce movements similar to a healthy knee with low energy consumption [25, 26]. The system is assembled in a lightweight and compact structure and can be used as a prosthetic knee, a knee actuator for exoskeletons and in robotic functions [30].

The MR Clutch and MR Brake of the AMRK present multi-disc configuration to improve the torque-to-mass ratio and compactness. With this configuration, the systems can work in full-slip and non-slip conditions. In the full-slip regime, there is a relative movement between the input and output and the torque is transmitted by the shear stress of the MR fluid [31], which is responsible for high heat generation. When in non-slip condition, there is no relative movement between the input

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*Transient Thermal Analysis of a Magnetorheological Knee for Prostheses and Exoskeletons…*

on the MR clutch and brake to avoid high working temperatures.

The AMRK configuration is presented in **Figure 1**. The system consists of a motor unit (MU) (EC 60 flat motor, harmonic reducer CSG-14-100-2a and MR clutch) mounted in parallel to an MR brake, and can work as a motor, clutch and brake. This configuration allows the actuator to be controlled independently by the MU or by the brake MR, exploring thereby the advantages of each subsystem. The device is supported by two main structures: The external structure connects to the upper part of the prosthesis/exoskeleton, the internal one connects to the lower part of the prosthesis/exoskeleton through adapters. A pair of thin section bearings allows relative movement between the external and internal structures. The structures are made of 7075 aluminum alloy [5], as shown in **Figure 1(a)**. **Figure 1(b)** displays the configuration of the MR clutch and MR brake. The

dynamic model of the AMRK is presented in **Figure 1(c)**, and the proposed actuator

The MR brake is housed between the external and internal structures and dissipates energy just when the knee joint should exert negative work during over-ground walking, operating mode I in **Figure 1(d)**. The MR brake is designed with a multi-disc configuration and hollow iron core to reduce mass and increase torque capacity [38], as displayed in **Figure 1(b)**. The output disks are connected to the aluminum cover, which is attached to the external structure of the actuator. The output disks are assembled interlayered with the input disks, which are attached to the iron core that is coupled to the internal structure. The MR fluid fills the space between disks. The magnetic field induced by the coil controls the yield stress of the MR fluid; in this way, the MR fluid can behave as a semi-solid or a Newtonian fluid depending on the action of the magnetic field. Consequently, the resistive torque of

operating modes for over-ground walking are shown in **Figure 1(d)**.

the brake is controlled by the input current on the brake coil [39].

**2. The active MR knee**

and output and the system works as a solid unit [32]. In this case, the heat generation is due just by Joule effect on the coil. The properties of the MR fluid strongly depend on the temperature, for this reason, the fluid shows different performances with the temperature variation [33]. The viscosity of the fluid changes with temperature variation, which results in a change in its shear stress. Moreover, MR fluids use additives to decrease sedimentation and increase the dispersion of particles, and such additives are also sensitive to temperature variation, some of it decompose when reaching about 100°C [34]. Moreover, cyclic operation under high and low temperatures can lead to irreversible changes in the MR fluid. It can run-out its rheological properties, leading to uncontrolled shear stress due to the influence of material agglomeration under magnetic field conditions [33]. Since high temperature deteriorates the MR fluid, the full-slip operation is the most critical working condition for the MR clutch and MR brake [35]. Some works in the literature present methodologies to evaluate how these properties change with temperature [36]. Chen et al. [33] proposed an experimental setup to evaluate an MR transmission under different temperatures, obtaining a set of torque and temperature curves with different current inputs. Zipster et al. [37] proposed an experimental setup that analyzes the MR fluid in flow mode, under different temperatures. Wang et al. [34] made a complete characterization of the MR fluid under different temperatures. Here we present a transient thermal analysis of the AMRK under over-ground working conditions to evaluate if the heat generation can deteriorate the MR fluid or be dangerous for the user. Since the full-slip operation increases heat production, we proposed an operating mode for the AMRK that minimizes the heat dissipation

*DOI: http://dx.doi.org/10.5772/intechopen.95372*

#### *Transient Thermal Analysis of a Magnetorheological Knee for Prostheses and Exoskeletons… DOI: http://dx.doi.org/10.5772/intechopen.95372*

and output and the system works as a solid unit [32]. In this case, the heat generation is due just by Joule effect on the coil. The properties of the MR fluid strongly depend on the temperature, for this reason, the fluid shows different performances with the temperature variation [33]. The viscosity of the fluid changes with temperature variation, which results in a change in its shear stress. Moreover, MR fluids use additives to decrease sedimentation and increase the dispersion of particles, and such additives are also sensitive to temperature variation, some of it decompose when reaching about 100°C [34]. Moreover, cyclic operation under high and low temperatures can lead to irreversible changes in the MR fluid. It can run-out its rheological properties, leading to uncontrolled shear stress due to the influence of material agglomeration under magnetic field conditions [33]. Since high temperature deteriorates the MR fluid, the full-slip operation is the most critical working condition for the MR clutch and MR brake [35]. Some works in the literature present methodologies to evaluate how these properties change with temperature [36]. Chen et al. [33] proposed an experimental setup to evaluate an MR transmission under different temperatures, obtaining a set of torque and temperature curves with different current inputs. Zipster et al. [37] proposed an experimental setup that analyzes the MR fluid in flow mode, under different temperatures. Wang et al. [34] made a complete characterization of the MR fluid under different temperatures. Here we present a transient thermal analysis of the AMRK under over-ground working conditions to evaluate if the heat generation can deteriorate the MR fluid or be dangerous for the user. Since the full-slip operation increases heat production, we proposed an operating mode for the AMRK that minimizes the heat dissipation on the MR clutch and brake to avoid high working temperatures.
