# Structure Design and Kinematics Analysis of a Novel Unpowered Load-Carrying Lower Extremity Exoskeleton with Parallel Topology

Authors: Qiang Yan; Jianjun Zhang; Kaicheng Qi
Journal: Mathematical Problems in Engineering
 (2018)

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## Abstract

A novel unpowered load-carrying parallel lower extremity exoskeleton is proposed. It is aimed at enhancing the load-bearing ability of the operator. Firstly, the structure of the novel exoskeleton is depicted in the second section; meanwhile, the degree of freedom concerning the exoskeleton is gotten by analyzing the number of links and the kinematic joints. Secondly, the forward position analysis of the exoskeleton for the swing leg is obtained. Using the expressions concerning the joints of knee and angle, the workspace of the swing leg in supporting gait circle is analyzed by the software of MATLAB. Thirdly, according to the schematic diagram of the mechanism, the static force analysis of the supporting leg for the exoskeleton is obtained. Finally, the static force of the supporting leg of the person who is not wearing the unpowered exoskeleton is gotten. Meanwhile, the genetic algorithm is used to get the optimum stiffness of the spring for energy-restoring device. By comparing the changes of force and torque for the supporting leg who is not wearing it and the skeleton which is worn by a person, some conclusions are carried out.


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## Body

## 1. Introduction

The load-carrying lower limb powered exoskeleton (LLPE) is a human-machine system. It can follow the human movement and provide assistance for people who carry many. Generally, the anthropomorphic designing structure is used to realize the motion space coupling between the operator and the exoskeleton. In recent years, unpowered load-carrying parallel lower extremity exoskeleton (ULLPE) has been enormously studied. Compared with load-carrying lower limb powered exoskeleton, unpowered load-carrying lower extremity exoskeleton possesses merits such as smaller energy consumption, lighter weight, lower manufacturing cost, and higher stiffness, in addition to the inherent advantages of the general load-carrying lower limb powered exoskeleton in terms of bigger energy consumption, lower stiffness, higher manufacturing cost, and lower load to weight ratio. A novel ULLPE is the focus of the current trend in the research community, and various forms of LLPE have been presented.In 1960, the first human exoskeleton (Hardiman) was developed by general motors and mainly used for easing the fatigue of soldiers in USA. But it has a heavy body, a large volume, and only a single powered arm. In the 2000s, BLEEX [1], which was designed at the University of California, is to make exoskeleton easier for wearers to carry heavy objects. A military-assisted exoskeleton called HULC [2] which comprised an external driven motor was produced in the Berkeley bionic technology company in 2009. It can assist the human body to run at the speed of 11km/h at a negative weight of 90kg, but the endurance is short. In the 1980s, Cavagna, Kaneko, and others who were from Italy analyzed the body biomass utilization of different state of human walking and came to a conclusion that the energy that can be wasted during human walking is put forward to help the body walk. James Walsh et al. called the process human body energy storage strategy [3–7]; the progress can be described that, in the process of walking, the muscles can store part of gravitational potential energy and in the process of the human body movement next release walking load to reduce the human body. Human energy storage strategy can be used to make good use of the wasting energy of human muscle storage and walking, which is of great significance for the improvement of human walking ability. Steven H. and others [8] designed an unpowered exoskeleton and some experiments were carried out to identify the results of theory. In 2016, Donghai et al. [9] presented the design and analysis of a passive body weight- (BW-) support lower extremity exoskeleton (LEE) with compliant joints to relieve compressive load in the knee. The new design fully used the energy of human muscle storage and walking and promoted the development of unpowered exoskeletons. Recently, the design, kinematic, and dynamic problems including position analysis, singularity analysis workspace, and force analysis of the exoskeleton have been investigated by Cuan-Urquizo [10]. Emmanouil Spyrakos Papastavridis introduced PDD and PPDD control schemes combined with gravity compensation, which have improved the development of strategies that permitted COMAN to achieve walking trajectories. Dongming Gan and Jian S. Dai proposed a unified inverse dynamics model of a metamorphic parallel mechanism with pure rotation and pure translation phases; their work mainly gives good optimal design and control of the mechanism designed by them in various applications using two phases. Besides these exoskeletons mentioned above, some other exoskeleton architectures can be found in the literature [11–15].In this paper, a novel unpowered 8-DOF exoskeleton with four degrees of translational freedom and four degrees of rotational freedom is presented. It should be pointed out that seldom ULLPE can be designed in this way, this is also one novel contribution in this paper. The paper’s structure is arranged as follows. Firstly, the structure characteristics and DOFs of this exoskeleton are analyzed based on analyzing the number of links and the kinematic joints in Sections2 and 3, respectively. The workspace of the mechanism for the exoskeleton is obtained based on the forward position analysis in Section 4, and using computer code programming, several shapes of the reachable workspace of the exoskeleton are obtained in Section 5. Furthermore, the static performance analysis of the mechanism is analyzed by the balance force analysis between limbs in Section 6.1. Then, Section 6.2 presents the optimum stiffness of the spring for energy-restoring device by the genetic algorithm, and the static force of the supporting leg of the person who is not wearing the unpowered exoskeleton is gotten with the aim of comparing the changes of force and torque before and after wearing the exoskeleton in Sections 6.3 and 6.4, respectively. Lastly, Section 7 summarizes the full paper.


## 2. An Unpowered Exoskeleton and Its Structure Characteristics

As shown in Figure1, the structure of the ULLPE which was formulated is of symmetry and the two legs both have the identical kinematic characteristics. Therefore, one of legs is taken as the study object. The proposed unpowered exoskeleton mainly comprised upper supporting plate, upper limb link, postsupporting link, connection link, energy-restoring part, and lower supporting plate. Here, meanwhile, as seen in Figures 2 and 3, the swing leg comprises two branches chains. A variable stiffness energy storage device with 12 parts is designed. The detailed structure is shown in Figure 2. Here, upper cylinder link and the lower cylinder link form a moving pair, and the long spring with a large diameter and a small stiffness is installed at the inner wall of the lower connecting rod of the guide cylinder, and the short spring is set under the guide cylinder. The short spring guide rod crosses the short spring center with a large diameter and a large stiffness to fit with the guide bar block, so as to achieve the initial compression of the short spring and exert the pretightening force. The swing leg is analyzed and the schematic model of that is depicted in Figure 2. Considering the complex situation of the external exoskeleton, we restrict the working circumstance in the sagittal plane. As shown in Figure 1, we well know the comparison of the simple leg, such as the angle, knee, and the hip. The designation is satisfying the significant motions when people are walking. The swing leg has two branch chains: one is connected byR- R- R- R and the other byR- R -CS- R. Here,R, CS represent the revolute joint and energy-containing device. For the proposed mechanism, the structure with parallel topology is just moving in the sagittal plane and the CS can restore the energy which comes from the kinetic energy of individuals. It consists of two compressed springs and can lower the load of the load-carrying persons. Firstly, the schematic model of the swing leg is depicted in Figure 3. Locating the coordinate systemO-xyattached to postsupporting withO, linkOA1 with thexaxes is consistent withOA1 andyaxes are perpendicular to theOA1 andO is the origins. The signsLb,L1,L2, L3, L1, L4,andL5 represent the length of the linesOA1, A1A2, A2A3, A3A4,andA6A3respectively. The angles are expressed in Figure 3. It is important to note that β is the angle between the vectorA6A3 and the vertical direction and β1 between the vectorA6A5 and the vertical direction.Figure 1
CAD model of the proposed unpowered exoskeleton.Figure 2
CAD model of the energy-storing device.Figure 3
The schematic model of the swing leg.


## 3. Mobility Analysis

The degree of freedom of the mechanism is determined by the combined effect of the four limb constraint forces/couples. In this paper, counting the number of the joints and links is used to analyze mechanism. As well-known for us, a link has 3 freedoms and revolute joint has one freedom in a simple plane. Here, a simplification for CS is taken to analyze the freedom. The CS can be considered as a prismatic joint and has one translational degree.(1)F=∑i=1pi∗pi-L∗λiHere, L=p-n+1,n denotes the number of the links,p represents the number of the freedoms of every joint, andiis the code of the link, respectively.From (1), according to the analysis of the mechanism concerning the swing leg, n=9,λ=3,p=10, we can see that the swing leg limb owns 4 degrees. Considering the complex of the exoskeleton and in order to simplify the analysis, here, we take the hip link as the static link. As depicted in Figure 2, the number of the links has 9 links, and the amounts of revolute joints are 8 and being seen as a prismatic joint. So according to formula (1), the degree of freedom of the swing leg is 4; therefore, the ULLPE has 8 degrees. So, the simple leg owns two degrees of rotational freedom and two degrees of translational freedom.


## 4. Forward Position Analyses

The forward position analysis of the swing leg is concerned with ensuring the angle pose given the limb lengths. Initially, drawing the schematic model of the swing leg, the position of swing leg concerning the sagittal plane is obtained by using closing-vector-circle method. Here, the coordinates of the center of the knee are (x, y), and the coordinates of the center of the ankle are (x1, y1). The expressions can be described with the closed loop method:(2)OA→3=OA→1+A1A→2+A2A→3(3)OA→3=OA→6+A6A→3The formulas can be rewritten as follows:(4)OA6A3x=lb+l×sinθ1+l2×sinθ2+θ1(5)OA1A2A3x=l4×cosα+l5×sinβ(6)OA1A2A3y=l4×sinα+l5×cosβ(7)OA6A3y=l1×cosθ1+l2×cosθ1+θ2Meanwhile, according to Figure 3,L5is a constant, so the constrain condition can be depicted as follows:(8)A6A3=l5According to (2)-(8), the coordinates of the angle and knee can be ensured.(9)cos⁡α=lb+l1×sin⁡θ1+l2×sin⁡θ1+θ21l4(10)sin⁡β=A-B1l5Here,(11)A=lb+l1×sin⁡θ1+l2×sin⁡θ1+θ2B=l1×cos⁡θ1+l2×cos⁡θ1+θ2The pose of the knee is depicted as follows:(12)x=lb+l1×sin⁡θ1+l2×sin⁡θ1+θ2(13)y=l1×cos⁡θ1+l2×cos⁡θ1+θ2So, the coordinates of the angle in the sagittal plane can be described as follows:(14)x1=lb+l1×sin⁡θ1+l2×sin⁡θ1+θ2+l3×sin⁡θ3-θ1-θ2(15)y1=l1×cos⁡θ1+l2×cos⁡θ1+θ2+l3×cos⁡θ3-θ1-θ2According to formulas (2)-(14), we can see that, for the proposed ULLPE in this paper, the forward position analyses of the mechanism can be calculated directly though analytical method; the location of the joints for the knee and ankle, which is enormously significant for doing some research in workspace, can be obtained.


## 5. Workspace Analysis

In this section, the workspace of the swing leg and the reachable workspace of the simple ULLPE are obtained based on the forward position analysis. From Section4, we can see that given a set of limb rotations angles θ1θ2θ3, the other parameters including pose coordinates can be calculated directly by corresponding equations. So, when the restrictions to the link rotation angles are set up, the swing leg motion workspace and the reachable workspace of the mechanism can be obtained. Here, the workspace of the knee joints and the angle joints are analyzed, respectively.


### 5.1. Case Studies on the Workspace of the Knee Joint and Ankle Joint

In order to explore the relationships between the series of parameters and the mechanism, we define some parameters values. The architectural parameters of the ULLPE exoskeleton are selected aslb=100 mm,l1=300 mm,l2=500 mm,l3= 600 mm,l4= 550 mm,l5= 150 mm,0≤θ1≤pi/4, 0≤θ2≤pi/4, and θ3=pi/4. Here, the spectrum of the knee concerning the leg is depicted in the Figures 4(a), 4(b), 5(a), and 5(b). The workspace of the manipulator can be generated by a MATLAB program. The reachable workspace of the ankle for the exoskeleton is shown in Figures 6(a), 6(b), 7(a), and 7(b).Figure 4
The reachable workspace of the knee joint concerning the swing leg.
(a) (b)Figure 5
The reachable workspace of the knee joint concerning the swing leg.
(a) (b)Figure 6
The reachable workspace of the ankle joint concerning the swing leg.
(a) (b)Figure 7
The reachable workspace of the ankle joint concerning the swing leg.
(a) (b)According to given the parameter and the simulation, Figures5, 6, and 7 show us the basic shape concerning the swing leg. The reachable workspace of the swing leg can be seen from the above images.


### 5.2. Case Studies on the Workspace of the Swing Leg for the Exoskeleton

The approach followed in this paper for having an insight into the reachable workspace of the swing leg considers the workspace of the knee and angle joints and the distribution between each parameter. Figures4 and 5 show that the distribution ofy andx only has relation with the θ1 and θ2, regardless of the variation of θ3. Figures 6 and 7 depict that the distribution ofy1 andx1 only has relation with the θ1 and θ2, regardless of the variation of θ3. Figure 8 demonstrates that the distribution ofy1 andx1 only has relation with they andx, and the parameters, including all the values of they andx andy1 andx1, are altogether exhibited in the three-dimensional space.Figure 8
The distribution of the parameter concerning x, x1, y, and y1.
(a) (b) (c)


## 5.1. Case Studies on the Workspace of the Knee Joint and Ankle Joint

In order to explore the relationships between the series of parameters and the mechanism, we define some parameters values. The architectural parameters of the ULLPE exoskeleton are selected aslb=100 mm,l1=300 mm,l2=500 mm,l3= 600 mm,l4= 550 mm,l5= 150 mm,0≤θ1≤pi/4, 0≤θ2≤pi/4, and θ3=pi/4. Here, the spectrum of the knee concerning the leg is depicted in the Figures 4(a), 4(b), 5(a), and 5(b). The workspace of the manipulator can be generated by a MATLAB program. The reachable workspace of the ankle for the exoskeleton is shown in Figures 6(a), 6(b), 7(a), and 7(b).Figure 4
The reachable workspace of the knee joint concerning the swing leg.
(a) (b)Figure 5
The reachable workspace of the knee joint concerning the swing leg.
(a) (b)Figure 6
The reachable workspace of the ankle joint concerning the swing leg.
(a) (b)Figure 7
The reachable workspace of the ankle joint concerning the swing leg.
(a) (b)According to given the parameter and the simulation, Figures5, 6, and 7 show us the basic shape concerning the swing leg. The reachable workspace of the swing leg can be seen from the above images.


## 5.2. Case Studies on the Workspace of the Swing Leg for the Exoskeleton

The approach followed in this paper for having an insight into the reachable workspace of the swing leg considers the workspace of the knee and angle joints and the distribution between each parameter. Figures4 and 5 show that the distribution ofy andx only has relation with the θ1 and θ2, regardless of the variation of θ3. Figures 6 and 7 depict that the distribution ofy1 andx1 only has relation with the θ1 and θ2, regardless of the variation of θ3. Figure 8 demonstrates that the distribution ofy1 andx1 only has relation with they andx, and the parameters, including all the values of they andx andy1 andx1, are altogether exhibited in the three-dimensional space.Figure 8
The distribution of the parameter concerning x, x1, y, and y1.
(a) (b) (c)


## 6. The Spring Stiffness Optimization on Exoskeleton

In this section, the stiffness of spring is acquired to optimize for enhancing the function of the exoskeleton performance. Firstly, the analysis of the supporting leg for the exoskeleton is worked out based on the static force analysis between links. Secondly, the conditions of stiffness constrain are listed. The most reasonable stiffness of the spring for the energy-storing is obtained. Thirdly, in order to make a comparison of force and torque before and after wearing exoskeletons, we make an analysis on our body and draw some equations when we do not wear it. Finally, some variation curves are shown by software. Meanwhile, some conclusions are carried out.


### 6.1. Calculation of Joint Torque on Exoskeleton

The description of the forces exerted on every limb for supporting leg is shown in Figure9.Figure 9
Forces analysis of every limb on the supporting leg.From Figure9, the force direction exerted every limb can be seen. According to the balance of the whole exoskeleton structure, the equations can be obtained and listed as follows:(16)α3=180∘-β1-β,α2=90∘+β1-α,F6=F5=K×lkt-lk1While the spring 2 is compressed, the force F5 and F6 can be rewritten as follows:(17)F5=F6=K×lkt-lk1+K2×lkt-2×lk1+lk2-h2+l2×K2(18)F0=F5×sin⁡α3sin⁡πα2+α3,F9=sin⁡α2sin⁡πα2+α3×F5,F1x=F0×cos⁡α(19)Fbag=F1y+F0×sin⁡α,F1x=F2x=F3x=F4x,F1y=F2y=F3y=F4yHere,Fbag,Fz,Fm represent the weight of the bag, ground support force, and the friction from the ground, respectively.Based on (17), (18), (19), and (20), the torques from each joint can be calculated(20)M1=Fbag×lb-F0×lb×sinα(21)M2=M1+F1y×sinθ1+F1x×cosθ1×l1(22)M3=M2+F2y×sinε+F2x×cosε×l2(23)M4=M3+F3x×cosη-F3y×sinη-F9x×sinβ×cosη+F9y×cosβ×sinη×l3Here,η=θ3-θ2-θ1, ε=θ2+θ1, γ=0∘, lb is the distance between the mass center of the bag and the human body, andK1,K2 are the two spring’s stiffness, respectively.


### 6.2. Simulation Conditions, Parameter Settings, and Optimization Results

Here, while optimizing the spring stiffness, it should also meet the following constraints:( 1 ) The stiffness of the spring is bigger than zero.( 2 ) During a gait cycle, the torque of the knee joint should be lowered after optimization.( 3 ) The torque of the lumbar joint is always positive.The constrain conditions can be described by some equations:(24)fk=∑i=1nM1in+M2n+M3n+M4n(25)minfkK1>0,K2>0,M1>0Mb2>Mf2,T b 2 indicates the torque provided by the knee joint in the previous support cycle, and Tf2 stands for the torque offered by the knee in the last support cycle;f(k) is the sum of the finite torque which is from the human body within a gait cycle; here, a supporting cycleT is divided intoN equipartition;N is just one of portions in a supporting cycleT. By adding up all the effective torques applied to every moment of the whole support period, the total effective torque from the human body is acquired. By optimization, the effective torque is minimized by the human body in the support cycle of the whole gait.The optimization of the stiffness of the exoskeleton spring can be optimized by adopting genetic algorithm. It is known that the pending unit is a variable stiffness energy storage element with pretightening force. It can compress only one spring in the early stage and the middle period of support, and two springs must be compressed at the last stage of support. The second spring is a large rigid spring with preload, and the optimized parameters arex1(k1), x2(k2), x3(lk2),andx4(h2). The MATLAB genetic algorithm optimization toolbox is used to solve the stiffness optimization model. The parameters of the toolbox are set as follows.The number of populationNp=200, the maximum evolutionary algebraPc=200, the cross-probabilityNm=0.6, and the mutation probabilityNm= 0.01, as shown in the objective function and constraint formulas (25) and (26). The layout optimization schematic diagram is shown in Figure 10.Figure 10
Optimization flowchart of the spring for energy-storing device.By the optimization method proposed in the paper and with the help of the software (MATLAB), the optimal solution of the optimal parameter is obtained, as shown in Table1.Table 1
Optimal solution of optimal parameters.
K 1 K 2 l k2 h 2 5.1 N/mm 7.0 N/mm 420 mm 28 mm l k2   is the original length of spring 2, and h2 is the initial compression quantity of spring 2.


### 6.3. Calculation of Joint Torque on Human Body

Similarly, as depicted in Figure11, the coordinate systemOxy is established at the origin ofO, and the lower limb statics of human body is as follows:(26)F1x=0F1y=Fbag=Fzy(27)F1y=F2y=F3y=F4yF1x=F2x=F3x=F4xFigure 11
Pressure angles between each link.Among them,Fbag is the weight of the load, and lb1 andl1~l3 are the distance from the load center to the human body and the length of the human body segments, respectively.Fzy is the counterforce of the support side.The torque is provided by the joints of the human body.(28)M1b=Fbag×lb1,M2b=M1b+Fbag×l1×sin⁡θ1(29)M3b=M2b+Fbag×l2×sin⁡ε(30)M4b=M3b+Fbag×l3×sin⁡ηwhereM1b~M4b represents the torque provided by the waist, hip, knee, and ankle joints from human body.θ1~θ3 represents the motion angles of the human lower extremities, andθ = θ3-θ2-θ1,ε= θ1+θ2.


### 6.4. Comparative Torque Analysis before and after Wearing

The torque applied to the waist, hip, knee, and ankle joints in a support period is calculated according to the formulas when the human body is not wearing the exoskeleton. In order to compare joint torque before and after wearing exoskeleton the torque provided by the human body's waist, hip, knee, and ankle joints is calculated when the human body is wearing the exoskeleton. During the entire gait support cycle and before and after wearing the exoskeleton, the torques provided by the waist, hips, knees, and ankle joints are compared (the torque is negative, which is indicating that the human joints provide the reverse direction torque). The average value of the torque applied to each joint of the human body during the entire gait support period is obtained, and the total effective torque exerted on each joint of the human body is also obtained. According to calculation in a supporting gait cycle, the waist and hip joint torques were reduced by about 42% and 40%, and the knee joint torque was reduced by about 3%, but the ankle joint torque was slightly increased about 9%. The total effective torque of the lower limb joints for the human body can be reduced by 16% when the exoskeleton is on load. The comparison of joint torque before and after wearing exoskeleton is depicted in Figure12. The hip, waist, knee, and ankle joint torque saving ratio in a supporting gait cycle are shown in Figures 13–16. At the same time, the total torque savings in a supporting gait cycle are shown in Figure 17.Figure 12
Comparison of joint torque before and after wearing exoskeleton.Figure 13
Waist joint torque saving ratio.Figure 14
Hip joint torque saving ratio.Figure 15
Knee joint torque saving ratio.Figure 16
Ankle joint torque saving ratio.Figure 17
Total torque savings in a supporting gait cycle.


## 6.1. Calculation of Joint Torque on Exoskeleton

The description of the forces exerted on every limb for supporting leg is shown in Figure9.Figure 9
Forces analysis of every limb on the supporting leg.From Figure9, the force direction exerted every limb can be seen. According to the balance of the whole exoskeleton structure, the equations can be obtained and listed as follows:(16)α3=180∘-β1-β,α2=90∘+β1-α,F6=F5=K×lkt-lk1While the spring 2 is compressed, the force F5 and F6 can be rewritten as follows:(17)F5=F6=K×lkt-lk1+K2×lkt-2×lk1+lk2-h2+l2×K2(18)F0=F5×sin⁡α3sin⁡πα2+α3,F9=sin⁡α2sin⁡πα2+α3×F5,F1x=F0×cos⁡α(19)Fbag=F1y+F0×sin⁡α,F1x=F2x=F3x=F4x,F1y=F2y=F3y=F4yHere,Fbag,Fz,Fm represent the weight of the bag, ground support force, and the friction from the ground, respectively.Based on (17), (18), (19), and (20), the torques from each joint can be calculated(20)M1=Fbag×lb-F0×lb×sinα(21)M2=M1+F1y×sinθ1+F1x×cosθ1×l1(22)M3=M2+F2y×sinε+F2x×cosε×l2(23)M4=M3+F3x×cosη-F3y×sinη-F9x×sinβ×cosη+F9y×cosβ×sinη×l3Here,η=θ3-θ2-θ1, ε=θ2+θ1, γ=0∘, lb is the distance between the mass center of the bag and the human body, andK1,K2 are the two spring’s stiffness, respectively.


## 6.2. Simulation Conditions, Parameter Settings, and Optimization Results

Here, while optimizing the spring stiffness, it should also meet the following constraints:( 1 ) The stiffness of the spring is bigger than zero.( 2 ) During a gait cycle, the torque of the knee joint should be lowered after optimization.( 3 ) The torque of the lumbar joint is always positive.The constrain conditions can be described by some equations:(24)fk=∑i=1nM1in+M2n+M3n+M4n(25)minfkK1>0,K2>0,M1>0Mb2>Mf2,T b 2 indicates the torque provided by the knee joint in the previous support cycle, and Tf2 stands for the torque offered by the knee in the last support cycle;f(k) is the sum of the finite torque which is from the human body within a gait cycle; here, a supporting cycleT is divided intoN equipartition;N is just one of portions in a supporting cycleT. By adding up all the effective torques applied to every moment of the whole support period, the total effective torque from the human body is acquired. By optimization, the effective torque is minimized by the human body in the support cycle of the whole gait.The optimization of the stiffness of the exoskeleton spring can be optimized by adopting genetic algorithm. It is known that the pending unit is a variable stiffness energy storage element with pretightening force. It can compress only one spring in the early stage and the middle period of support, and two springs must be compressed at the last stage of support. The second spring is a large rigid spring with preload, and the optimized parameters arex1(k1), x2(k2), x3(lk2),andx4(h2). The MATLAB genetic algorithm optimization toolbox is used to solve the stiffness optimization model. The parameters of the toolbox are set as follows.The number of populationNp=200, the maximum evolutionary algebraPc=200, the cross-probabilityNm=0.6, and the mutation probabilityNm= 0.01, as shown in the objective function and constraint formulas (25) and (26). The layout optimization schematic diagram is shown in Figure 10.Figure 10
Optimization flowchart of the spring for energy-storing device.By the optimization method proposed in the paper and with the help of the software (MATLAB), the optimal solution of the optimal parameter is obtained, as shown in Table1.Table 1
Optimal solution of optimal parameters.
K 1 K 2 l k2 h 2 5.1 N/mm 7.0 N/mm 420 mm 28 mm l k2   is the original length of spring 2, and h2 is the initial compression quantity of spring 2.


## 6.3. Calculation of Joint Torque on Human Body

Similarly, as depicted in Figure11, the coordinate systemOxy is established at the origin ofO, and the lower limb statics of human body is as follows:(26)F1x=0F1y=Fbag=Fzy(27)F1y=F2y=F3y=F4yF1x=F2x=F3x=F4xFigure 11
Pressure angles between each link.Among them,Fbag is the weight of the load, and lb1 andl1~l3 are the distance from the load center to the human body and the length of the human body segments, respectively.Fzy is the counterforce of the support side.The torque is provided by the joints of the human body.(28)M1b=Fbag×lb1,M2b=M1b+Fbag×l1×sin⁡θ1(29)M3b=M2b+Fbag×l2×sin⁡ε(30)M4b=M3b+Fbag×l3×sin⁡ηwhereM1b~M4b represents the torque provided by the waist, hip, knee, and ankle joints from human body.θ1~θ3 represents the motion angles of the human lower extremities, andθ = θ3-θ2-θ1,ε= θ1+θ2.


## 6.4. Comparative Torque Analysis before and after Wearing

The torque applied to the waist, hip, knee, and ankle joints in a support period is calculated according to the formulas when the human body is not wearing the exoskeleton. In order to compare joint torque before and after wearing exoskeleton the torque provided by the human body's waist, hip, knee, and ankle joints is calculated when the human body is wearing the exoskeleton. During the entire gait support cycle and before and after wearing the exoskeleton, the torques provided by the waist, hips, knees, and ankle joints are compared (the torque is negative, which is indicating that the human joints provide the reverse direction torque). The average value of the torque applied to each joint of the human body during the entire gait support period is obtained, and the total effective torque exerted on each joint of the human body is also obtained. According to calculation in a supporting gait cycle, the waist and hip joint torques were reduced by about 42% and 40%, and the knee joint torque was reduced by about 3%, but the ankle joint torque was slightly increased about 9%. The total effective torque of the lower limb joints for the human body can be reduced by 16% when the exoskeleton is on load. The comparison of joint torque before and after wearing exoskeleton is depicted in Figure12. The hip, waist, knee, and ankle joint torque saving ratio in a supporting gait cycle are shown in Figures 13–16. At the same time, the total torque savings in a supporting gait cycle are shown in Figure 17.Figure 12
Comparison of joint torque before and after wearing exoskeleton.Figure 13
Waist joint torque saving ratio.Figure 14
Hip joint torque saving ratio.Figure 15
Knee joint torque saving ratio.Figure 16
Ankle joint torque saving ratio.Figure 17
Total torque savings in a supporting gait cycle.


## 7. Conclusions

This paper proposes a novel unpowered lower extremity 8-DOF exoskeleton. Initially, the degree of freedom on the mechanism is ensured by analyzing the number of links and kinematic pairs. Then, according to the schematic diagram of the mechanism, the forward position analysis of the structure is carried out, such as the motion expressions of the knee and ankle joints. Then, based on these equations, the workspace of the knee and ankle is described by the software of MATLAB. Thirdly, in order to improve the performance of the exoskeleton, two springs of energy-restoring device in the mechanism are optimized by adopting genetic algorithm. So, the most suitable stiffness is acquired. Finally, the static force of the supporting leg for the person who is not wearing the unpowered exoskeleton is gotten with the aim of comparing the changes of force and torque before and after wearing the exoskeleton; meanwhile, some conclusions are drawn. Based on the kinematics analysis of the mechanism, the inverse/forward dynamics analyses, the stiffness performance analysis, and the other kinematic optimization of the mechanism will be investigated in the future work.



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