**4.2. Powered ankle and toe with compliant actuators**

As discussed above, we finally used two series elastic actuators (SEA) to construct ankle and toe joints. Each SEA includes a DC motor, a transmission and a spring structure. Compared with other actuators, SEA has several benefits: 1) the actuator exhibits lower output impedance and back-driveability; 2) shock tolerance is greatly improved by the spring placed in series between the transmission and the load; 3) the motor's required force is reduced; 4) force control stability is improved, even in intermittent contact with hard surfaces; 5) energy can be stored and released in the elastic element, potentially improving efficiency [31, 45]. The design of the two SEAs will be introduced in details in the following part of the paper.

The design of the powered joints is based on the functionality of human toe and ankle joints. As shown in Fig. 6, the basic architecture of the segmented foot is an integration of two SEAs, which are used to drive the ankle and toe joints respectively. Each SEA comprises a DC motor, a ball screw transmission and a spring structure. Because human toe joint only outputs net positive work at the moment TO, the toe joint is designed to rotate counterclockwise passively, 10 Will-be-set-by-IN-TECH

**Figure 6.** Schematics diagram of the segmented foot with compliant joints. The two main components of

air storage system. Thus, several recent studies try to change air muscles into motor-spring

In addition, there are other types of compliant actuators in robotics. For example, shape memory alloys show impressive actuation characteristics, while suffer from slow response and motion constraints [40]. Other interesting compliant actuators include artificial muscle actuator using fluid [41], polymer materials [42], dielectric elastomers [43], etc. Most of them are used in particular environments and difficult to implement in autonomous systems,

As mentioned above, currently, spring based compliance is the most promising compliant actuators in the field of dynamic walking. By using the proper spring based elastic mechanisms, lower-limb prostheses and exoskeletons may be capable of performing stable walking on different terrains and with controllable walking velocity. Applying compliant actuators to lower-limb rehabilitation systems provides not only new challenges for bipedal

As discussed above, we finally used two series elastic actuators (SEA) to construct ankle and toe joints. Each SEA includes a DC motor, a transmission and a spring structure. Compared with other actuators, SEA has several benefits: 1) the actuator exhibits lower output impedance and back-driveability; 2) shock tolerance is greatly improved by the spring placed in series between the transmission and the load; 3) the motor's required force is reduced; 4) force control stability is improved, even in intermittent contact with hard surfaces; 5) energy can be stored and released in the elastic element, potentially improving efficiency [31, 45]. The design of the two SEAs will be introduced in details in the following part of the paper.

The design of the powered joints is based on the functionality of human toe and ankle joints. As shown in Fig. 6, the basic architecture of the segmented foot is an integration of two SEAs, which are used to drive the ankle and toe joints respectively. Each SEA comprises a DC motor, a ball screw transmission and a spring structure. Because human toe joint only outputs net positive work at the moment TO, the toe joint is designed to rotate counterclockwise passively,

the prosthesis are two SEAs, which are used to drive the ankle and toe joints respectively.

systems as compliant actuators for dynamic walking systems, e.g. [39].

especially in lower-limb prostheses and exoskeletons.

locomotion but also improvement of practical use.

**4.2. Powered ankle and toe with compliant actuators**

**Figure 7.** The ankle joint can be simplified as a special three-bar mechanism, of which the length of c can be modulated by SEA 1.

and to rotate clockwise actively. When toe joint is forced to rotate counterclockwise, Spring 2 will be extended to store energy. At the moment TO, Spring 2 will release the stored energy and Motor 2 will drive the toe joint to rotate clockwise via Transmission 2 and Spring 2. Spring 2 comprises four drawsprings set in parallel and the stiffness is 200*N*/*cm*. Motor 2 used in the current design is a 30*W* DC motor with an angle encoder.

The functionality of the human ankle joint can be realized by a special three-bar mechanism, shown in Fig.10. The special three-bar mechanism comprises three bars (*a*, *b* and *c*) and three hinges (*A*, *B* and *C*). Hinge *A* is the ankle joint. Bars *a* and *b* are the foot and the shank respectively. *c* is a special bar, of which the length can be regulated by SEA 1. *θ*<sup>1</sup> is the angle of the ankle joint, which is used to control the movement of the ankle. *θ*<sup>1</sup> can be calculated by the following equation:

$$\theta\_1 = \arccos \frac{L\_a^2 + L\_b^2 - L\_c^2}{2L\_a L\_b} - \theta\_3 \tag{15}$$

where *La*, *Lb* and *Lc* are the length of the bars *a*, *b* and *c* respectively. *La* and *θ*<sup>3</sup> can be calculated by *L*<sup>3</sup> and *H*1:

$$\theta\_3 = \pi - \arctan \frac{L\_3}{H\_1} \tag{16}$$

$$L\_a = \sqrt{L\_3^2 + H\_1^2} \tag{17}$$

where *L*<sup>3</sup> is the level distance of the ankle joint from the end of the heel and *H*<sup>1</sup> is the height of the ankle joint from the ground. *Lc* is determined by SEA 1. When Spring 1 is compressed or pulled by Transmission 1 (the nut of the ball screw, Nut 1, move upward), the *Lc* becomes shorter. When Spring 1 is extended or pushed by Transmission 1 (Nut 1 move downward), the length of c becomes longer. In fact, the state of Spring 1 and the movement of Transmission 1 are not independent, namely, *Lc* is determined by a combined motion of Spring 1 and Transmission 1. *Lc* can be obtained by the following equation.

$$L\_{\rm c} = L\_{\rm s} + L\_{\rm t} + \frac{F}{K\_1} + \Delta\_1 \tag{18}$$

Where *Ls* is the length of Spring 1 with no load. *Lt* is the length of Transmission 1 with the nut at the initial position; *F* is the load on Spring 1, which is determined by the weight of the subject and the walking state; *K*<sup>1</sup> is the spring stiffness of Spring 1. Δ<sup>1</sup> is the displacement of the nut of Transmission 1.

**Figure 8.** The CAD model and the prototype of PANTOE 1 with compliant joints and segmented foot. The prototype is made of aluminium-alloy. The weight is 1.47 kg (not including the Li rechargeable battery about 1 kg), comparable to the weight of the subject's limb. The full angles of the ankle and the toe joints are 45*<sup>o</sup>* and 90*<sup>o</sup>* respectively.
