Design and analysis of a novel fall prevention device for lower limbs rehabilitation robot

Abstract

BACKGROUND:

Most stroke survivors are suffering from physical motor impairments and confronting with the risk of falls, and well trunk stability is essential for balance during daily functional activities.

OBJECTIVES:

Current fall prevention devices have various limits to the efficient recovery of balance function of the trunk. To provide hemiplegic patients after stroke with the retraining of trunk position sense and a safety environment, a novel fall prevention device is proposed.

METHODS:

Firstly, the structure of the device is introduced and this work is a first effort towards restoring trunk balance function through retraining of trunk position sense. Secondly, the kinematic and static model of the device are developed. Lastly, kinematic and static analysis are carried out to study the motion characteristics, and a contrast experiment was derived to show the effectiveness of robot.

RESULTS:

No obvious difference in balance ability between two groups prior treatment ( $P>$ 0.05). Fugl-Meyer assessment in all the cases were improved in different extent ( $P<$ 0.05). The robot group had significantly higher Fugl-Meyer scores after treatment than the control group ( $P<$ 0.05).

CONCLUSIONS:

The results show that the fall prevention device has good kinematic dexterity within the prescribed workspace and markedly improves balance function.

Keywords

Trunk position sense kinematics fall prevention device statics force field

1. Introduction

Trunk stability requires appropriate muscle strength and neural control as well as sufficient position sense to provide a stable foundation for movement [1]. Most paralytics with movement disorder suffer from balanced dysfunction, which seriously affects the recovery of their walking ability [2]. And 5,000,000 people leave permanent disability by stroke every year [3], hidden danger of falls hinders stroke survivors from the advanced therapies, retraining of trunk position sense is a method for improving the balance and control of the trunk [4]. Although the six motion parameters determine the gait pattern rather than the trunk control, but the trunk control is important to balance, functional performance and fall prevention. Therefore, a fall prevention device with position and force feedback for the trunk has become necessary in balance function rehabilitation and trunk muscle strength training.

Three types of fall prevention device have been used for the safety protection in rehabilitation training: walking stick assistant devices, fall prevention safety harness and partial body weight support system. For example, the walking-aid robot developed by the Huazhong university of science and technology uses multi-sensor to recognize motion intention, which remains the center of gravity in the scope of protection [5]; Fall prevention safety harness is adopted by the CAREN rehabilitation system [6] and the KineAssist rehabilitation robot [7], which catch the patient when the tilted angle of trunk exceeds a certain value to reduce the risk of falls; Body weight support system is adopted by the Locomat rehabilitation robot [8] and the ReoAmbulator gait training robot, which almost completely limits the motion of trunk, without the risk of falls. Furthermore, the Solo-Step [9], SafeGait and RevoGait have been used for lower limbs rehabilitation training, which provide patients a safe environment and a boost of confidence [10].

However, some limitations of these designs are the following, walking stick assistant devices cannot ensure the safety of patients, fall prevention safety harness has little contribution to trunk position feedback and correction, body-weight support system limits the motion of trunk and pelvis.

In the following study, a novel fall prevention device concentrated on retraining of trunk position sense is developed, as shown in Fig. 1. The improvements over the previous solutions are the following. 1) The device actualizes three degrees of freedom (DOFs) of the trunk, trunk flexion-extension, lateroflexion and rotation; 2) Based on the kinematics and statics of the device, the safety motion space of the trunk is obtained; 3) Establishing the relation between the position and force feedback of trunk, stroke survivors can recognize the trunk position and enhance the balance ability through retraining of trunk position sense and the perturbation-based balance training respectively [11, 12]. The device changes the flexion-extension, lateroflexion and rotation of pelvis, two of them are the determinant grades for gait pattern.

In this paper, we integrate fall prevention device with the retraining of trunk position sense to effectively improve the quality of trunk balance rehabilitation. The analysis of kinematics and statics can be used to obtain the safety workspace and the feedback forces acting on patient. These results can then be used to analyze the movement trajectory and static perturbation.

Table 1
Motion range of the trunk

Motion	The largest motion range
Flexion-extension ( $\alpha$ )	4.66 $\sim$ 9.24 ${}^{\circ}$
Lateroflexion ( $\beta$ )	2.63 $\sim$ 4.07 ${}^{\circ}$
Rotation ( $\gamma$ )	6.93 $\sim$ 14.7 ${}^{\circ}$

Figure 1.

The mechanism of the fall prevention device on the rehabilitation robot.

2. Materials and methods

2.1 System description and kinematic modeling

As a fall prevention device, it is particularly important for assuring the security, comfortableness and effectiveness of the rehabilitation training [13]. The motion rules of trunk can be simplified as three rotations around $X$ , $Y$ and $Z$ axis, actual motions are more complicated than this, Table 1 shows the statistical data of the motion range of the trunk [14]. Therefore, the fall prevention device needs to achieve the rotations around three axes and limit the motion range. It is also required to provide the patients with force feedback during movement to ensure the implementation of the retraining of trunk position sense.

The CAD model of the mechanism is shown in Fig. 2. There are three main components of the mechanism: Fixed base: It is the fixed part of the mechanism and bolts to the pelvis support mechanism [15]. Joint 1 realizes the initial adjustment of lateroflexion and the rotation around $Y$ axis through a sort of nested institution, the joint space of joint 1 is $\pm$ 15 ${}^{\circ}$ , and we can control joint 1 through a plunger. Planar four-bar mechanism: Regarding the trunk as a rigid body, three links and the trunk constitute the planar four-bar mechanism, the connection between the trunk and the device is completed by braces. It realizes the flexion extension motion around $X$ axis and limits the flexion-extension range by the safety rope. Rotation part: It is an arc slide rail and its rotation center coincides with the center of trunk. It realizes the rotation motion around $Z$ axis, the joint space of joint 5 is $\pm$ 18 ${}^{\circ}$ .

There are two sets of springs to provide the static perturbation: Compressed springs: They are installed on either side of the joint 1. The length of one spring decreases when the $\beta$ changes, then it generates a reset force to remind patient about the correct position. Elastic ropes: They are installed on either side of the joint 2. The length of the elastic ropes decreases when $\alpha$ increases, self-weight of the mechanism generates a reset force. The length of the elastic ropes increases when $\alpha$ decreases, elastic force generates a reset force.

In order to verify the rotation angle relation of each joint during movements, and obtain the corresponding relation between the position transformation of trunk and static perturbations acting on the patient, thus providing basis for the optimization design of the fall prevention device and determination of the spring parameters, the kinematics and statics modeling of the fall prevention device are required. In this paper, the analytical method is used for the computation of kinematics, the results are used for static analysis.

Figure 2.

The model of the fall prevention device.

Figure 3.

The diagram and coordinates systems of the fall prevention device.

Figure 3 shows the general configuration of the fall prevention device, where the base reference coordinates $O_{b}x_{b}y_{b}z_{b}$ and the end coordinate $O_{e}x_{e}y_{e}z_{e}$ locate in the fixed base of the fall prevention device and the center of pelvis respectively, with $O_{e}$ as the rotating center of the pelvis. We define trunk $l_{4}$ as a rigid-body here, then the end effector of the fall prevention device has three DOFs limited by the pelvis support mechanism. The rotation matrix ${}^{b}R_{e}$ is the transformational matrix between the reference coordinate and the end coordinate. Here $Z$ - $X$ - $Y$ Euler angles are adopted to describe rotation $\alpha$ around $X$ axis, $\beta$ around $Y$ axis and $\gamma$ around $Z$ axis of the reference coordinate. When the angles of rotations are given, ${}^{b}R_{e}$ can be expressed as Eq. (1).

$^{b}R_{e}=R(Z,\gamma)R(Y,\beta)R(X,\alpha)$ (1)

Forward kinematics is to express the trunk orientation $(\alpha,\beta,\gamma)$ by the joint angle $\theta_{i}(i=$ $1,$ $2,$ $3,$ $4,$ $5)$ . For the fixed base and rotation part, if the magnitude of $l_{1}$ is small enough and ignoring the trunk shape of patient, the amounts of lateroflexion and rotation can be expressed as Eqs (2) and (3).

$\displaystyle\beta=\theta_{1}$ (2) $\displaystyle\gamma=\theta_{5}$ (3)

Inverse kinematics is to solve angles of each joint $\theta_{i}(i=$ $1,$ $2,$ $3,$ $4,$ $5)$ for given trunk orientation $(\alpha,$ $\beta,$ $\gamma)$ . The approximated trajectory of the trunk orientation in a gait cycle is shown in Fig. 4. For the four-bar mechanism, $\vec{l}_{2}$ , $\vec{l}_{3}$ , $\vec{l}_{4}$ and $\vec{l}_{5}$ denote the vector of each bar in plane $O_{e}y_{e}z_{e}$ . The kinematics of four-bar mechanisms has been extensively treated, a detailed explanation is in [16]. This work focuses on analyzing the mechanism position, accordingly, the closed loop equation can be expressed as:

$\vec{l}_{2}+\vec{l}_{3}=\vec{l}_{4}+\vec{l}_{5}$ (4)

Assuming the magnitude of $\vec{l}_{1}$ is zero and applying polar notation to each term of Eq. (4):

$l_{2}e^{i\theta_{2}}+l_{3}e^{i\theta_{3}}=l_{5}+l_{4}e^{i\alpha}$ (5)

Using the equation of Euler on Eq. (5) and separating real and imaginary

Figure 4.

The approximated motion rules of trunk in a gait cycle.

parts:

$\left.{\begin{array}[]{*{20}c}l_{3}\cos\theta_{4}={-l}_{4}\cos\alpha+l_{5}\cos% \theta_{b}+l_{2}\cos\theta_{2}\\ l_{3}\sin\theta_{4}={-l}_{4}\sin\alpha+l_{5}\sin\theta_{b}+l_{2}\sin\theta_{2}% \\ \end{array}}\right\}$ (6)

Solving Eq. (6), and define:

$\displaystyle a_{34}=2(l_{4}\cos\alpha-l_{5})l_{2}/[{(l_{4}\cos\alpha-l_{5})}^% {2}$ $\displaystyle\mspace{44.0mu }+l_{4}^{2}\sin^{2}\alpha+l_{2}^{2}+l_{3}^{2}]$ (7) $\displaystyle b_{34}=2{l_{2}l}_{4}\sin\alpha/[{(l_{4}\cos\alpha-l_{5})}^{2}+l_% {4}^{2}\sin^{2}\alpha$ $\displaystyle\mspace{44.0mu }+l_{2}^{2}+l_{3}^{2}]$ (8) $\displaystyle w_{34}=a_{34}^{2}+b_{34}^{2}$ (9)

Then, we can obtain the joint angle of the four-bar mechanism:

$\displaystyle\theta_{2}=\sin^{-1}\frac{(b_{34}-a_{34}\sqrt{w_{34}-1})}{w_{34}}$ (10) $\displaystyle\theta_{4}=\sin^{-1}\frac{l_{2}(b_{34}{-}a_{34}\sqrt{w_{34}-1})-w% _{34}l_{4}\sin\alpha}{w_{34}l_{3}}$ (11) $\displaystyle\theta_{3}=\theta_{2}-\theta_{4}$ (12)

When the motion rules of trunk are given as shown in Fig. 4, we can obtain the change rules of joint angles $\theta_{i}(i=1,2,3,4,5)$ in a gait cycle, as shown in Fig. 5. The results of inverse kinematics indicate the motion ranges are less than the joint spaces of each joint, which means the fall prevention device satisfies the motion requirements of trunk. And the results of inverse kinematics will be used in calculation of statics.

Figure 5.

Change rules of each joint in a gait cycle.

2.2 Statics modeling

There are two purposes for the statics modeling: calculating the constraining force in kinematic pair of the mechanism, determining the spring coefficient of compressed spring and elastic rope; solving the corresponding relation between the position transformation of trunk and static perturbations acting on the patient. Under normal circumstances, the kinematic acceleration is small enough, accordingly, statics analysis is representative.

Figure 6.

Statics model of the four-bar mechanism.

In order to study the force $F_{Y}$ acting on the patient along $Y$ axis due to the flexion-extension movement, we establish the equilibrium equation of four-bar mechanism by applying virtual work principle, as shown in Fig. 6. The elastic ropes generate $F_{r}$ along $O_{3}A$ , and the system reaches complete static equilibrium under the moment $M$ and mechanism self-weight. Calculating all equilibrium position and configuration through analysis of this model, then we can certain direction and magnitude of the force $F_{Y}$ . For the equivalent four-bar mechanism depicted in Fig. 6, assuming that moment $M$ generated by the force $F_{Y}$ balances the moment $M_{2}$ generated by the force $F_{r}$ and mechanism self-weight. According to the principle of virtual work [17]:

$\delta U=\sum\limits_{i=2}{m_{i}g\delta\vec{z}_{i}}+\sum\limits_{i=2}{M\delta% \vec{\theta}_{i}}$ (13)

$\vec{z}_{i}$ are virtual displacements of each bar. The force $F_{r}$ generated by the elastic ropes can be written as Eq. (14), $l_{0}$ is the shortest length of the elastic ropes.

$F_{r}=k_{2}\Delta l_{r}=k_{2}\left(\sqrt{l_{2}^{2}{+}l_{e}^{2}-2l_{1}l_{e}\cos% \theta_{1}}-l_{0}\right)\!\!$ (14)

As seen in Fig. 6, with forces and moments, the system reaches static equilibrium, i.e., $\delta U=0$ , we can obtain the expression of static equilibrium equation:

$\displaystyle m_{2}g\delta z_{2}+m_{3}g\delta z_{3}+m_{4}g\delta z_{4}+M_{2}% \delta\theta_{2}$ $\displaystyle\quad∼{}+M_{4}\delta\theta_{4}=0$ (15)

Where $\delta z_{2}=l_{2}\sin\theta_{2}\delta\theta_{2}/2$ , $\delta z_{3}=-(l_{4}\sin\theta_{4}\delta\theta_{4}+l_{2}\sin\theta_{2}\delta% \theta_{2})/2$ , $\delta z_{4}=l_{4}\sin\theta_{4}\delta\theta_{4}/2$ , $M_{2}=F_{r}$ $\sin\theta_{r}l_{2}$ , $M=F_{Y}l_{4}$ . Substituting these expressions back into Eq. (2.2) and simplifying it, the relation between force $F_{Y}$ and component parameter can be written as Eq. (2.2).

$\displaystyle F_{Y}=\frac{m_{3}g}{2}\left(\sin\theta_{4}+\frac{l_{2}\sin\theta% _{2}\delta\theta_{2}}{l_{4}\delta\theta_{4}}\right)$ $\displaystyle\quad∼{}-\frac{m_{2}gl_{2}\sin\theta_{2}\delta\theta_{2}}{2l_{4}% \delta\theta_{4}}-\frac{m_{4}g\sin\theta_{4}}{2}$ $\displaystyle\quad∼{}-\frac{F_{r}\sin\theta_{r}l_{2}\delta\theta_{2}}{l_{4}% \delta\theta_{4}}$ (16)

In order to study the force $F_{X}$ acting on the patient along $X$ axis due to

Figure 7.

Statics model of the fall prevention device.

the lateroflexion movement, we establish the equilibrium equation of the fall prevention device by applying Newton second law, the joints 2, 3, 4 and 5 are supposed to be fixed, as shown in Fig. 7. The compressed springs generate $F_{c}$ along $Z$ axis. From $\sum M_{O_{1}}=0$ , we have:

$F_{X}l_{4}-\frac{mgl_{5}\sin\theta_{1}}{2}+F_{c}l_{B}=0$ (17)

Where $F_{c}=k_{1}l_{B}\tan\theta_{1}$ . Then we can obtain the equilibrium equation about the force $F_{X}$ , $k_{1}$ and $\beta$ according to Eqs (2) and (17).

2.3 Experimental design and subjects

The actual field test was carried out in a rehabilitation hospital located in Jiaxing, China, Jul. 2016 $\sim$ Sep. 2016. Thirty-six patients suffering from hemiplegia were chosen and randomly divided into two groups, one using our robot and the other using a conventional method. There were no significant differences in age, gender, contralateral hemiplegia, course of disease and clinical nerve function assessment between the two groups ( $P>$ 0.05).

Regular physical training was conducted in both groups, the control group adopted conventional rehabilitation method, 4 times per week and 30 minutes every time, 8 weeks in total. The robot group was provided exercise training with the device, 4 times per week and 30 minutes every time, 8 weeks in total. The Fugl-Meyer assessment was employed to check the results.

Figure 8.

Curves of three angles in a walk cycle.

3. Results

MALAB is adopted to program the subprogram of kinematics and statics analysis for fall prevention device respectively. When the patient is instructed to gait training, bringing movement parameters of trunk into the corresponding subprogram, then we can obtain the acquired joint space and the force field in workspace. The contrast experiment in the Jiaxing rehabilitation hospital, balance training with the robot vs. traditional rehabilitation training was carried out to test the effectiveness of the device. All experimental data was processed with SPSS 22.0, and expressed in mean $\pm$ standard deviation, independent-samples $T$ test was employed in data comparison.

3.1 Simulation analysis

Assuming the motion rules of patient is the rules shown in Fig. 4, when the joint angles $\theta_{i}(i$ $=$ $1,$ $2,$ $3,$ $4,$ $5)$ from the inverse kinematics are given, the orientation of the trunk in a gait cycle is shown in Fig. 8, where the motion ranges of the end effector can be computed as listed in Table 2.

Table 2
Motion range of the end effector

Orientation	Motion Range/ ${}^{\circ}$
$\alpha$	$-$ 5.73 $\sim$ 9.6
$\beta$	$-$ 5.73 $\sim$ 5.73
$\gamma$	$-$ 17.2 $\sim$ 17.2

In order to choose the appropriate elastic coefficient of the elastic ropes, thus providing patient appropriate feedback force in motion space. According to kinematics and statics model, we present the simulation for the force conditions in workspace. According to Eqs (2.1) and (14), by varying the elastic coefficient of the elastic ropes from 0 to 2000 N/m, and the motion rule of flexion-extension movement is

$\alpha=A_{\alpha}\sin\left(\frac{2\pi t}{T}+\theta_{\alpha}\right),$

where $A_{\alpha}$ is the motion amplitude of trunk around $X$ axis, $\theta_{\alpha}$ is the initial phase, $T$ is the gait cycle [18]. Consequently, the force $F_{Y}$ acting on patient in a gait cycle is shown in Fig. 9.

Figure 9.

Statics solution illustration in a gait cycle.

Figure 10.

Reset force illustration in a gait cycle.

Figure 11.

Relationship among $F_{\textit{resultant}},\alpha$ and $\beta$ .

Figure 9 shows that the designed mechanism works as expected when $k_{2}=995$ N/m, the force $F_{Y}$ is almost zero when patient is in the equilibrium position, and the other characteristic is that the device provides reset force when the patient deviates away from the equilibrium position. In addition, the relationship between the reset force and the flexion-extension movement is approximately linear.

Table 3

Patient data

Participant information of patients $(x\pm s)$
Group	Number	Age	Gender		Hemiplegia		Onset	Equilibrium level	Weight
			Male	Female	Left	Right	(Month)
Robot	18	47.4 $\pm$ 20.0	10	8	9	9	2.94 $\pm$ 2.4	1.5 $\pm$ 0.8	65 $\pm$ 13
Conventional	18	54.0 $\pm$ 14.3	9	9	8	10	2.5 $\pm$ 1.5	1.25 $\pm$ 0.9	63 $\pm$ 10

According to Eqs (2) and (17), by varying the elastic coefficient of the elastic ropes from 0 to 1000 N/m, and the motion rule of lateroflexion movement is

$\beta=A_{\beta}\cos\left(\frac{2\pi t}{T}+\theta_{\beta}\right),$

where $A_{\beta}$ is the motion amplitude of trunk around $Y$ axis, $\theta_{\beta}$ is the initial phase, $T$ is the gait cycle. Consequently, the force $F_{X}$ acting on patient in a gait cycle is shown in Fig. 10. Figure 10 shows that the designed mechanism works as expected when $k_{1}\geqslant 600$ N/m, the compressed springs can overcome the adverse moment generated by the self-weight of the mechanism, the mechanism provides reset force when the patient deviates away from the equilibrium position. In addition, the relationship between the reset force and the lateroflexion movement is linear.

Determining the elastic coefficients of springs, $k_{2}=995$ N/m and $k_{1}=650$ N/m, the motion rules of the trunk is shown in Fig. 4. When $\gamma$ is zero, the simulation of resultant feedback force is carried out in the workspace. We can obtain the magnitude and direction of the resultant force, as shown in Fig. 11.

Table 4

Comparison of Fugl-Meyer assessment of two groups ( $x\pm s$ )

Group	Number	Prior treatment	8 weeks after treatment
Robot group	18	17.37 $\pm$ 4.17 ${}^{*}$	26.88 $\pm$ 8.24 ${}^{**,\dagger}$
Control group	18	16.00 $\pm$ 1.93	18.13 $\pm$ 1.13

Compared with the control group before treatment: ${}^{*}$ $p>$ 0.05; Compared in group before treatment: ${}^{**}$ $p<$ 0.01; Compared with control group: ${}^{\dagger}$ $p<$ 0.05.

3.2 Contrast experiment

The patient data is given in Table 3. Table 4 and Fig. 12 show the results of the field test. Boxplot was employed to show the dispersion of our dataset. Nattier blue bar showed the data of robot group and mazarine showed another group. There is no obvious difference in balance ability between two groups prior treatment ( $P>$ 0.05). Fugl-Meyer assessment in all the cases were improved in different extent ( $P<$ 0.05). The robot group had significantly higher Fugl-Meyer scores after treatment than the control group ( $P<$ 0.05). It can be seen from Fig. 12 that training with our robot yields a much better improvement.

Figure 12.

Comparison of Fugl-Meyer assessment before and after treatment.

4. Discussion

By comparing Table 2 with Table 1, motion range of the end effector is greater than that of the trunk. In addition, the three rotation centers are basically in coincidence with the motion center of the trunk. Therefore, the fall prevention device meets the requirements of trunk’s motions, providing the premise for the implementation of rehabilitative strategy.

According to Fig. 11, in any pose the patient exposures to the reset force pointed to the initial equilibrium position. And $F_{\textit{resultant}}$ increases with the movement deviation from the equilibrium position, the patient can judge the validity of the motion and affirm the best motion trail with the force field. In addition, the reset force forms a conical force field which protects the patient from falls and rigid impact, and the device will catch the patient if the trunk’s deviation reaches a certain level.

Balance function is an important ability to automatically adjust and maintain the posture in movement or exposing oneself to perturbed force. The trunk plays an important role in posture balance. Retraining of trunk position sense is a method for improving the balance and control of the trunk. The proposed device provides patients an intervention in balance training and a secure environment, the experimental results showed the robot can markedly improve balance function of the subjects, comparing with the control group. Granacher et al. discussed the relationships between trunk muscle strength and balance performance in older adults [11], the device can provide subjects with force field to reinforce the trunk muscle strength. As a next step of this research, dynamic balance and trunk muscle activation will be measured.

5. Conclusion

To solve the existing problems of the fall prevention devices, a novel fall prevention device based on retraining of trunk position sense has been studied, which can be applied to carry out the trunk strength training, position sense training and fall prevention. Kinematic analysis and simulations of the fall prevention device showed that the mechanism can satisfy the needs of the rehabilitative training of the trunk. Static analysis and simulations of the mechanism showed that the mechanism can provide appropriate feedback force to assist the patients in the judgment of motion correctness and protect patient from falls. All results indicate that the fall prevention device has finely kinematic character and is suitable for the retraining of trunk position sense. The contrast experiment shows the effectiveness of trunk’s balance training.

In the future, we plan to extend the balance training in the force-field to study the relation between learning and field strength.

Footnotes

Acknowledgments

This work was supported by the National Natural Science Foundation of China (Grant No. 61573234) and the Shanghai Municipal Science and Technology Commission (Grant No. 17511107800).

Conflict of interest

None.

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