**2. The active MR knee**

*Heat Transfer - Design, Experimentation and Applications*

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

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

**1. Introduction**

**374**

functions [30].

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

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

**Figure 1.**

*The AMRK configuration and operation modes. (a) Cutaway view of the actuator. (b) configuration of the MR clutch and MR brake. (c) Dynamic model of the system. (d) Operating mode for over-ground walking used in the transient thermal analysis.*

Active torque of the AMRK is required just when the knee exerts positive work, operating mode II in **Figure 1(d)**, and it is produced by the MU that comprises an EC motor, a harmonic drive (HD) and an MR clutch. The motor and HD stators are attached to the internal structure and the HD output is connected to the iron core of the MR clutch. The MR clutch has the same working principle as the MR brake, that is, when the magnetic field is activated, the MR fluid yield stress increases and prevents the relative movement between input and output disks. Thus, the torque produced by the motor-reducer is transferred to the external structure of the actuator controlled by the input current on the clutch coil. During swing phase, the knee rotates freely achieving high angular velocity. It can be accomplished by the AMRK as long as the MU is deactivated and the MR brake exerts low resistive torque to stabilize the joint, operating mode III in **Figure 1(d)**.

The torque supported by the MR brake and clutch follows the shear equation of a fluid between disks with relative angular movement [40], as shown below:

$$T = \bigcap\_{r \atop r \atop 1}^{n} \tau\_{MR} r\_D dA \tag{1}$$

**377**

**Table 1.**

*MR brake and MR clutch variables.*

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

τ

> ϕ π

saturation in any elements of the magnetic circuit.

**Variable Optimal Value**

*r*o [mm] 54 *r*i [mm] 48.5

*T* [N m] 35.0 55.4

*N* [gaps] 14 20 *B*MR [T] 0.45 0.50 *I* [A] 2.1 1.8 *N*t [turns] 164 226 *τ*y [kPa] 27.3 30.3 *R*c [ohm] 4.34 6.05 *P* [W] 19.2 19.6 *M* [kg] 0.37 0.46

design variables after optimization process.

π

( ) ( ) *<sup>Y</sup> MR TN rr rr o i o i <sup>h</sup>* = −+ − 3 3 4 4 2 3 4

where *τ*y is the yield stress of the MR fluid, which is a function of the magnetic field strength and can be obtained from the manufacturer's catalog, *μ*MR is the MR fluid viscosity, *h* is the gap thicknesses and *ω* is the angular velocity of

As the magnetic circuit is composed by a set of elements in series, the magnetic flux is uniform throughout the circuit [41]. As the desired value for the magnetic flux density in the MR fluid area (*B*MR) is a design parameter, the magnetic flux can

= − ( *r rB o i MR* ) 2 2

Similarly, the magnetic flux of a given circuit can also be described as a function of the number of coil's turns (*N*b), the current (*I*) and the equivalent reluctance of

> *b eq N I R*

It worth noting that Eqs. (3) and (4) are just valid as long as there is no magnetic

Eqs. (1)–(4) are used to construct a parametrized model to optimize the design variables (see [5]) for more details). **Table 1** presents the optimized value of the

**MR Brake MR Clutch**

ϕ

ωµ

(2)

(3)

= (4)

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

the disks.

be described as follows:

the circuit (*R*eq) [41]:

where *τ*MR is the shear stress of the MR fluid, *r*D is the radius of the disks, and *A* is the effective contact area between disks and MR fluid. The contact area can be described in terms of the number of gaps (*N*) filled by the MR fluid, and the internal (*r*i) and external (*r*o) radii of the disks. In addition, MR fluids behave like an ideal plastic fluid or Bingham plastic when subjected to magnetic field. Then the previous equation can be rewritten as:

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

$$T = 2N\pi \left[ \frac{\tau\_Y}{3} \left( r\_o^3 - r\_i^3 \right) + \frac{\phi \mu\_{\rm MR}}{4h} \left( r\_o^4 - r\_i^4 \right) \right] \tag{2}$$

where *τ*y is the yield stress of the MR fluid, which is a function of the magnetic field strength and can be obtained from the manufacturer's catalog, *μ*MR is the MR fluid viscosity, *h* is the gap thicknesses and *ω* is the angular velocity of the disks.

As the magnetic circuit is composed by a set of elements in series, the magnetic flux is uniform throughout the circuit [41]. As the desired value for the magnetic flux density in the MR fluid area (*B*MR) is a design parameter, the magnetic flux can be described as follows:

$$
\varphi = \pi \left( \mathbf{r}\_o^2 - \mathbf{r}\_i^2 \right) B\_{\text{MR}} \tag{3}
$$

Similarly, the magnetic flux of a given circuit can also be described as a function of the number of coil's turns (*N*b), the current (*I*) and the equivalent reluctance of the circuit (*R*eq) [41]:

$$
\varphi = \frac{N\_b I}{R\_{eq}} \tag{4}
$$

It worth noting that Eqs. (3) and (4) are just valid as long as there is no magnetic saturation in any elements of the magnetic circuit.

Eqs. (1)–(4) are used to construct a parametrized model to optimize the design variables (see [5]) for more details). **Table 1** presents the optimized value of the design variables after optimization process.


#### **Table 1.**

*Heat Transfer - Design, Experimentation and Applications*

Active torque of the AMRK is required just when the knee exerts positive work, operating mode II in **Figure 1(d)**, and it is produced by the MU that comprises an EC motor, a harmonic drive (HD) and an MR clutch. The motor and HD stators are attached to the internal structure and the HD output is connected to the iron core of the MR clutch. The MR clutch has the same working principle as the MR brake, that is, when the magnetic field is activated, the MR fluid yield stress increases and prevents the relative movement between input and output disks. Thus, the torque produced by the motor-reducer is transferred to the external structure of the actuator controlled by the input current on the clutch coil. During swing phase, the knee rotates freely achieving high angular velocity. It can be accomplished by the AMRK as long as the MU is deactivated and the MR brake exerts low resistive torque to

*The AMRK configuration and operation modes. (a) Cutaway view of the actuator. (b) configuration of the MR clutch and MR brake. (c) Dynamic model of the system. (d) Operating mode for over-ground walking used* 

The torque supported by the MR brake and clutch follows the shear equation of a

*MR D ri T r dA* <sup>=</sup> ∫ τ

where *τ*MR is the shear stress of the MR fluid, *r*D is the radius of the disks, and *A* is the effective contact area between disks and MR fluid. The contact area can be described in terms of the number of gaps (*N*) filled by the MR fluid, and the internal (*r*i) and external (*r*o) radii of the disks. In addition, MR fluids behave like an ideal plastic fluid or Bingham plastic when subjected to magnetic field. Then the

(1)

fluid between disks with relative angular movement [40], as shown below:

*ro*

stabilize the joint, operating mode III in **Figure 1(d)**.

previous equation can be rewritten as:

**376**

**Figure 1.**

*in the transient thermal analysis.*

*MR brake and MR clutch variables.*
