Developing of a wearable ankle rehabilitation robotic device

2.1. Common ankle and foot injuries and their solution

The ligaments of the ankle may be excessively stretched or even torn when the foot is tucked, due to or without external force. Such injuries often occur in sports. Acute ankle injuries are most common. They account for 15 to 20 % of sports injuries. Sports that use frequent, rapid changes in direction, jumps and contact with other players pose a particular risk to ankle ligaments. Football, basketball, and volleyball are sports with particularly high injury rates, such as acute ankle injuries. The risk of repeated ankle injuries is particularly high among athletes. Approximately one third of patients suffer a recurrent ankle injury within three years; 73 per cent of athletes do so. Later, many patients complain of slight swelling in the ankle area, pain during walking and running, swelling and some instability of the ankle joint. 85 % of ankle upper ligament injuries are lateral ligament injuries, of which front lateral ligaments are the most affected. There are also lower ankle injuries. Injuries to only the lower part of the ankle are rare; according to statistics, 10 % of patients with chronic ligament instability of the upper ankle also have instability in the lower part of the ankle.

Fig. 1a) Ankle joint and b) ankle planes and movements

a)

b)

Five common injuries to the foot and ankle:

– Achilles Tendonitis or Tear.

– Ankle Sprain.

– Stress Fractures of the Foot.

– Fractures of the Ankle.

– Plantar Fasciitis.

Ankle ligament injuries can be divided into 3 degrees of severity:

– I degree (light).

Ligament sprain without macroscopic rupture, slight swelling and/or sensitivity in the affected structures. Maintenance or minimal loss of function, usually no internal bleeding, no mechanical instability of the ankle, no problems with leg load.

– II degree (intermediate).

Partial macroscopic gap with moderate pain, swelling and sensitivity in affected structures. Slight or moderate impairment of function and mild or moderate instability of the ankle; often internal bleeding and problems with leg load.

– III degree (heavy).

Complete ligament rupture with pronounced edema and hematoma, increased pain sensitivity. Loss of ankle function, as well as pronounced abnormal movements and instability in the ankle, internal bleeding, inability to perform leg load.

Rehabilitation using robotic systems can have many advantages. It allows for more intensive and adapted rehabilitation activities and services (increasing the number and quality of therapy that can be prescribed) and allows all participants involved in the team (for example, physiotherapists, doctors, bioengineers, and others). Set and manage some operational parameters to make rehabilitation specific and optimal for the patient (type of exercise, level of robot assistance, strength, and kinematics that the patient should apply after the exercise).

2.2. Design of the 3 – RPS ankle joint robotic device

The presented robotic device can have a very complex design that drives the ankle joint. A person has many degrees of freedom in his legs, and this condition is difficult or even impossible to correct. The main joint of the foot and ankle joint, each of which provides smooth movements. The forces arising in these joints vary depending on the desired movement. Some movements, such as getting up from a sitting position, require not only significant efforts through the ankle joint, but also Coordination movement of the center of mass of the whole body. The repetition of all these forces and coordination movements is not a normal phenomenon. Thus, to reduce the complexity of the robot manipulator, it is created to bring only certain movements of everyday life [5-6].

The 3-RPS Ankle Rehabilitation manipulator is a robotic device designed to help patients recover from injuries or operations on the ankle joint. The device consists of three main components: a rotary joint, a prismatic joint, and a spherical joint. These joints work together to provide a range of motion that mimics the natural movement of the ankle joint, allowing patients to perform exercises that help strengthen and repair the joint. The device also includes sensors and control systems that track the patient's progress and adjust the movement of the joints accordingly [7, 8].

The 3-RPS parallel manipulator, in which various leg positions are considered (where $R$ is rotational, $P$ is prismatic and $S$ is spherical ligaments, respectively), has so far been studied in detail by many researchers. A 3-RPS parallel manipulator consisting of an equilateral platform was proposed by K. Hunt in 1983 [9-10].

3-RPS in a robot manipulator, only the ankle joint is involved, because it plays a key role in movement, requiring great strength, and is the main support.

The 3-RPS robot manipulator, designed to assist in the event of malfunctions, must be mobile. However, when creating this prototype, the device remains connected to avoid the need to connect wireless or on-board devices. This allows the use of standard controllers and real-time sensors and creates conditions for directing research to the algorithm that forms the basis of the 3-RPS robot manipulator. Like any design process, 3-RPS will have certain parameters that need to be considered and optimized when developing a robot manipulator.

The design of the 3-RPS parallel manipulator studied in this paper is shown in Fig. 2. This manipulator will have three RPS legs. Each foot consists of rotating, prismatic and spherical joints.

An important stage in the study of parallel structure mechanisms is their classification. The most popular are flat, translational-guiding, and spherical mechanisms.

Translational-guiding robotic systems are used in the operations of transferring and manipulating an object. At the same time, orienting movements are often not required, if they are necessary, then one degree of freedom can be added without changing the overall design of the manipulator.

Spherical robotic systems are in demand in processing operations of volumetric curved surfaces. If an additional linear degree of freedom is needed, it can be added without changing the overall design of the mechanism.

Classification of mechanisms for plane, translational and rotational movements was carried out using different groups of screws. To do this, we use the formula:

where $W$ – number of degrees of freedom; $D$ – the number of connections imposed by the $i$-th kinematic chain, $k$ – number of kinematic circuits $i=1,\dots .,k$:

where $n_i$ – the number of intermediate links located between the base and the output link, $p_{5i}$, $p_{4i}$, $p_{3i}$, $p_{2i}$, $p_{1i}$ – the number of kinematic pairs with 1, 2, 3, 4, 5 mobility in the $i$-th kinematic chain.

Fig. 23-RPS parallel manipulator mechanism

Classification and synthesis of parallel structure mechanisms can be carried out on the basis of Eq. (1), (2). Each kinematic chain contains a drive or imposes connections on the movements of the output link.

The classification is carried out according to the following criteria: the number of degrees of freedom $W$, the number of kinematic pairs, the number of imposed bonds by each chain. The first line indicates the number of kinematic chains and the number of connections imposed by this chain, the number in parentheses indicates the number of drive pairs in kinematic chains under which these numbers are located). Underlined numbers indicate chains with common connections (for spherical – all rotational pairs intersect at one point, for flat – three rotational; one translational two rotational; two translational and one rotational, all rotational are parallel, all translational).

Note that flat, translational-guiding, and spherical mechanisms correspond to closed three-membered groups of screws. In this regard, reduced formulas corresponding to a space equal to three can be used for them.

For the group under consideration, this can be expressed by the structural formula:

where $W$ – number of degrees of freedom, $D_i$ – the number of connections imposed by the $i$-th kinematic chain; $i=1,\dots k$; $k$ – the number of kinematic circuits.

The value $D_i$ is defined as:

where $n_i$ – the number of intermediate links located between the base and the output link.

Fig. 33-RPS parallel manipulator designs

The design of the 3-RPS parallel manipulator studied in this paper is shown in Fig. 3. This manipulator will have three RPS legs. Each foot consists of rotating, prismatic and spherical joints. The axes of the three rotating hinges intersect at point $A_1$. The coordinate system $x$, $y$, $z$, whose origin is at point O, is defined by ${\mathrm{\Sigma }}_0$ as a fixed frame. The base of the manipulator is limited by three rotating joints. Next, we use the projection coordinates to determine the location vectors of points $A_i$, where $i=$ 1, 2, 3. It is assumed that point $A_1$, is located on the $x$ axis, ${\epsilon }_1=$ 0°, and the coordinates of point $A_i$ and Vector $s_i$, expressed by ${\mathrm{\Sigma }}_0$, are expressed as follows:

The coordinate system $x$, $y$, $z$, where the coordinate head is located at point $Q$, is called ${\mathrm{\Sigma }}_1$, and it is attached to a movable platform. Three spherical joints are located at the top of the movable platform. the center of the $i$ spherical joint is denoted as $B_i$ ($i=$ 1, 2, 3).