Elsevier

Mechanism and Machine Theory

Volume 105, November 2016, Pages 31-43
Mechanism and Machine Theory

Evolutionary synthesis of mechanisms applied to the design of an exoskeleton for finger rehabilitation

https://doi.org/10.1016/j.mechmachtheory.2016.06.022Get rights and content

Abstract

To rehabilitate certain finger injuries, passive movement has proved to be positive. To help in this process, a physiotherapist's aid is necessary. In the last years, a series of exoskeletons have been presented that can move the finger in a controlled way, which can substitute the physiotherapist. However, these devices are not popular, mainly because of their high complexity and price. This work presents a simple, low-priced and easy-to-manufacture finger exoskeleton. These features make it possible to manufacture a customized device, so that it imitates each patient's natural finger movement accurately. In this paper, the whole process is explained, starting with the synthesis of the mechanism adapted to the patient's finger characteristics and finishing with the manufacturing of the exoskeleton with a 3D printer.

Introduction

In recent years, the use of mechanical systems for medical applications has increased notably. In the case of exoskeletons, mechanisms with links which move with a controlled relative movement between them are often used. Mechanism synthesis can be used to achieve the desired movement with the minimum number of degrees of freedom (dof). The reduction in the number of dof simplifies the control of the system and its complexity.

There is a variety of finger exoskeletons designed to help to rehabilitate when there are limitations in active finger movement [1], [2], [3]. Different studies have demonstrated the benefits of using these devices, by means of either active [4] or passive movement [5]. The main differences among them are related to their degrees of freedom, the number and type of sensors and the control used. There are exoskeletons that help to rehabilitate the finger in different cases, such as the recuperation of finger movement after a stroke [6], [7], [8], improvement in hand movement when the patient is affected by spine damage [9] and hand rehabilitation after an accident or flexor tendon surgery [2], [10], [11], [12], among others.

Most exoskeletons in the market are designed to recuperate hand movement after a stroke or spine damage. Usually, they have five fingers and include sensors to act according to the force carried out by the patient. Some of these devices use a virtual environment to create a great variety of motivating therapeutic exercises. These exoskeletons can be used for rehabilitation after an injury transmitting passive force. However, these devices are heavy and complex as they need one motor per dof. To avoid the weight of the motors on the hand, most of them transmit movement through cables that act over the hand.

There are a few exoskeletons specifically designed to rehabilitate hand movement after an accident or flexor surgery. These devices are focused on continuous passive movement (CPM) [5]. This therapy avoids arthrofibrosis on joints following trauma or surgery by repetitive passive slow motion. It starts with a short range of motion in the first sessions a few hours after surgery and increases it during the following days up to full range. As most injuries affect only one finger, many of these devices are developed to move just one finger. Some of them can be adapted to different hand sizes but none of them are custom manufactured adapted to each patient's phalanx lengths. Another limitation of the available devices is that they cannot be used as a splint to immobilize the finger, which would allow applying motion immediately after surgery.

In general, complex models of 24 dof are used to reproduce real movement of all five fingers. Depending on the variety and accuracy of the desired movements, devices with fewer dof can be used. This allows manufacturing less expensive and easier-to-control devices. Some authors propose the development of devices with 20 dof, which slightly simplifies the model but does not solve the complexity problem totally [13].

Some researchers have computed the error when using simpler models. Cobos et al. [14] evaluated the circular and prismatic grasping error for a simplified hand model with 9 dof. Results show error indexes close to 5.9% and 7.7% respectively when comparing it with a 24 dof model. The same evaluation for a hand with 6 dof shows errors close to 9.2% and 13.1% respectively.

After studying five subjects grasping 57 different objects and monitoring 15 joint angles of their fingers, Santello et al. [15] came to the conclusion that the angles between their phalanges were not completely independent from each other, suggesting that a hand has between 5 and 6 effective degrees of freedom.

In the case of a single finger, a 4-dof kinematic model is used to reproduce realistic finger movement; 3 degrees of freedom are used for each phalanx turn allowing flexion/extension and the fourth dof is used for adduction/abduction. However, when grabbing objects of different sizes, we tend to move the finger along different portions of a specific trajectory instead of following different trajectories [16].

This suggests that a finger exoskeleton with 1 dof could work properly for certain rehabilitation applications. The fact that there is only 1 dof affects the variety of movements but it does not affect movement accuracy. One point on a finger with 1 dof follows one predefined trajectory. However, if it had more degrees of freedom, it could follow different trajectories. Hence, in the first case the point follows a path while in the second case it can move in an area which is limited by a shape that defines the limits of finger movement. Nevertheless, this is not a handicap in an exoskeleton for rehabilitation with CPM as it is enough for the device to transmit flexion/extension motion to the finger, moving it along different portions of a specific path up to full range motion.

To ensure that a 1-dof exoskeleton follows patients' natural finger movement accurately, a mechanism synthesis process can be used. Not only does the synthesis of the mechanism have to take into account a desired path, but the phalanx angles during movement as well.

During the last 40 years a great effort has been carried out in computational synthesis of mechanisms. The great increase in computer power has allowed applying these methods to the minimization of goal functions. One of the first authors who studied these methods was Han [17], whose work was later improved by Kramer and Sandor [18] and Sohoni and Haug [19].

Recently, an increasing number of works have used evolutionary strategies to solve mechanism synthesis problems [20], [21], [22], [23], [24]. The main advantages of these methods are their simplicity in implementing algorithms and their low computational cost in some cases. One of the greatest challenges when these kinds of algorithms are used for synthesis of mechanisms is to find a good representation of the mechanisms. The first works using a genetic algorithm were carried out by Fang [20] and Ronston and Sturges [21]. Their algorithms used a binary representation of the mechanisms, whose processing procedures were time consuming and computationally expensive. Kunjur and Krishnamurty [22] used a real number representation of the mechanisms and incorporated a guided genetic operator reducing computing time and obtaining more accurate results. Cabrera et al. [23], [24] used a new evolutionary technique called Differential Evolution to solve a four-bar path mechanism synthesis obtaining very accurate results.

In the path generation synthesis, the coupler point traces a trajectory which is compared with the target trajectory. Then, an objective function is used to obtain the error between the desired and generated path. This function is generally formulated as the sum of squares of the differences between both trajectories [17], [18], [22], [23], [24].

In this work, a new 1 dof finger exoskeleton to enable rehabilitation after an injury or flexor tendon surgery is presented. The main advantages of the new design are:

  • Customizable according to the shape of patients' fingers. The exoskeleton is adapted to each patient's finger movement by means of an evolutionary technique for synthesis of mechanisms.

  • Simple to control and easy to manufacture.

  • Economic.

  • Can be used as a splint to immobilize the finger.

This paper is structured as follows: Section 2 explains the way to obtain the target path and the goal function. Section 3 is dedicated to defining the steps to be followed in order to obtain the results by means of an evolutionary algorithm. Section 4 explains the definition of the synthesis problem. Section 5 presents the results, which are used to create a 3D virtual model in a CAD-CAE parametric software application. This model allows simulating the movement of the exoskeleton, validating the design and manufacturing the device with a 3D printer. Section 6 shows the device and its control. Finally, discussion and conclusions are drawn in 7 Discussion, 8 Conclusions respectively.

Section snippets

Goal function

In this work, the mechanism shown in Fig. 1 is used to define the goal function. The finger is represented by bars L1, L2 and L3 and its end point follows the trajectory displayed in Fig. 1.

The mechanism has been designed looking for certain characteristics. The mechanisms of the exoskeletons mentioned above act on top of the finger while in our case the goal is to find a mechanism that wraps the phalanges. This allows using the exoskeleton as a splint to immobilize the finger after surgery

The MUMSA algorithm

Once the optimization problem has been explained in the previous section, an algorithm to solve the optimization problem is required. In this work an evolutionary algorithm is used [24]. The proposed algorithm, which is defined as Malaga University Mechanism Synthesis Algorithm (MUMSA), has the following three steps:

  • 1.

    The algorithm starts with the random generation of a starting population with NP individuals. For mechanism synthesis, the starting population is defined by sets of design variables

Definition of the problem

As described in Section 2, a set of target positions for the endpoint of the fingertip and phalanx angles have to be set to define the problem (see Table 2). The case discussed here is a path and motion generation synthesis problem without prescribed timing. The optimization problem is defined as follows:

  • Input parameters:

L1=52.7mm,L2=28.6mm,L3=18.44mm
  • Design variables:

χ=x0,y0,θ0,r1r2r3r4rACθACr5r6rDθDθCFθ21θ2N
  • Target points:

Fdi=90.037.96552.618.3955.291.6740.1182.3331.7852.5457.9813.01

Results

This section analyzes the results of the solution to our problem when applying the algorithm and the goal function developed previously. The entire algorithm proposed, including the genetic operators, has been run sequentially following the steps indicated in Section 3. Once the problem has been solved, we obtain the results shown in Table 3.

Fig. 6a shows that point F of the mechanism synthesized by means of the MUMSA algorithm follows the desired path (trajectory of the endpoint of the

The device

Once the solution to the synthesis problem has been obtained, we can create a virtual model of the exoskeleton. To do so, we have previously built a parametric model in CAD-CAM software with adjustable geometry depending on the values obtained for the mechanism design variables and the measurements of the patient's phalanges (Fig. 10a).

In Fig. 10b we can see the device manufactured with a 3D printer. The frame of the mechanism is located in the palm. The motor is fixed to the hand using a

Discussion

The customized exoskeleton presented in this paper is a new approach to the design of devices for finger rehabilitation after accidents or tendon surgery based on CPM. Current devices such as [2], [10], [12] have up to 4 dof and use force sensors. This makes them very flexible and functional for a variety of exercises but at the same time they are voluminous, heavy, complex and expensive. The use of mechanism synthesis with evolutionary algorithms gives way to the design of optimized

Conclusions

A customizable, low-priced exoskeleton for certain types of rehabilitation has been presented. The device can reproduce a patient's finger movement accurately thanks to the synthesis process followed to generate the exoskeleton mechanism. The input data and restrictions for the synthesis approach can easily be obtained by means of an X-ray of the injured finger and a video of the same finger of the healthy hand. The use of the MUMSA algorithm provides good results in little time with low

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