Coupling mechanism of spacesuit hip joint and thigh-femur for improved maneuverability of astronauts

Materials and Design 187 (2020) 108321

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Coupling mechanism of spacesuit hip joint and thigh-femur for improved maneuverability of astronauts Wang Zhen-Wei ⁎, Lin Dan-lan, Cheng Peng School of Aeronautics and Astronautics, University of Electronic Science and Technology of China, Chengdu 611731, People's Republic of China

H I G H L I G H T S

G R A P H I C A L

A B S T R A C T

• Proposed mechanism model embodies the coupling effect of thigh-femur and hip joint. • Introducing three coupling constraints constructs two-linkage mechanism for spacesuit hip joint. • Motion equations of hip joint are analytically established based on a vector graphic method.

a r t i c l e

i n f o

Article history: Received 1 September 2019 Received in revised form 19 October 2019 Accepted 29 October 2019 Available online 23 November 2019 Keywords: Coupling mechanism Motion analysis Hard hip joint Spacesuit

a b s t r a c t The spacesuit hip joint is a crucial component that helps with astronaut maneuvering activities such as walking and kneeling. The coupling mechanism of the hip joint with the thigh-femur, and its analytical solution, is less explored in this paper, a new hip joint and its coupling mechanism are designed. For this, based on the theory of machinery, five links, which represent the joint parts and the thigh-femur, and six joints are connected to develop the coupling mechanism. A cylindrical joint is adopted to avoid impact between the hip joint and thigh-femur. Three constraints are enforced to configure the proposed coupling mechanism. A specific mechanism of four links and five joints is constructed, which not only reduces one link but also possesses the analytical solution. Equations of motion of this mechanism are derived using vectors and verified via a case study. The vector graphic method is proposed for planar rotation decomposition of the joint parts. A prototype of the new mechanism is 3D printed and tested. Experiments reveal that new mechanism can work in any body orientation. In this way, the proposed coupling mechanism and vector graphic method help improve the spacesuit hip joint. © 2018 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).

1. Introduction

⁎ Corresponding author. E-mail address: [email protected] (W. Zhen-Wei).

Spacesuit development involves a diverse field of niche research topics, such as human–suit interaction [1], injuries estimation [2], torque analysis [3], human movements [4,5], and gait estimation [6,7]. As a crucial component of the spacesuit, the spacesuit hip joint enables an

https://doi.org/10.1016/j.matdes.2019.108321 0264-1275/© 2018 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).

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Upper plane Joint part 1 Hard hip joint Joint part 2 Rotational bearings Joint part 3 Lower plane

Joint part 4

(b)

(a)

Fig. 1. Conceptual model of (a) spacesuit and (b) hard hip joint.

astronaut wearing a pressurized spacesuit to perform maneuvering missions. Contemporary spacesuits include the Z series spacesuit [8], Mark III [9] and Bio-suit [10]. Generally, the spacesuit is pressurized with gas to a certain level, making it stiff in the vacuum of space [11]. However, the stiffening can greatly increase energy expenditure, impede mobility, alter the suit column, and stiffen the fabric as the joints bend [12]. As mentioned earlier, the hip joint of a spacesuit is central to the mobility required for astronaut activities such as walking, kneeling, etc. As humanity is on the cusp of a major breakthrough in manned planetary exploration, the spacesuit hip joint is becoming a central research focus. The hip joint can be broadly classified into flat-pattern joint, bellows joint, and rotation-bearing joint. Related research in this field includes performance testing [13,14], computational method [15,16], human factors [17,18], and structure development [19,20]. Although widely researched [21,22], the development of the spacesuit hip joint's mechanism and motion analysis have encountered several problems. Especially, there are no conclusive reports elucidating the coupling mechanism of the hard hip joint and thigh-femur. Moreover, few research works in the literature provide accurate analytical solutions of the hip joint motion. Interestingly, the mechanism is one of the important tools for the design, estimation, and analysis of the spacesuit hip joint. Moreover, an analytical solution would be more accurate and efficient than a numerical solution (the latter producing only approximate results). This paper proposes a coupling mechanism for the hard hip joint and the thigh-femur, and produces an accurate analytical solution of the hip-joint motion. 2. Coupling mechanism of hip joint and thigh-femur 2.1. Conceptual model of hard hip joint The spacesuit and hard hip joint designed for this study are illustrated in Fig. 1. The four joint parts are made of an aluminum

alloy and have similar structure. They are sequentially connected by rotational bearings. These bearings enable the joint parts to rotate independently. Thus, Joint part 4 can direct any spatial orientation. Similarly, Joint parts 1 and 4 are connected to the spacesuit by rotational bearings (not displayed in the conceptual model). When an astronaut wearing a spacesuit moves their thigh-femur, the hip joint will be derived to rotate. Consequently, the hip joint and thigh-femur move synchronously. This enables the astronaut to carry out activities such as surface maneuvers, planetary exploration, spacewalks etc. Based on empirical design, a hemispherical-shell-shape is adopted for the joint part design, as shown in Fig. 2. In order to form a connecting interface, the shell is cut into two parts by an inclination plane. The lower part is considered as the joint part. For convenience of mounting rotational bearings, grooves are respectively drilled in the upper and lower planes (not displayed in figure). The main characteristic of the joint part is its simple structure, and therefore it can be parameterized with ease. Form Fig. 2, it can be seen that the joint part is represented by a sphere radius of ri and an inclination angle of ai; where, subscript i is the index of the joint parts, i = 1, 2, 3 and 4. Above all, the relative rotation between joint parts is the fundamental driver of the hip-joint mobility. Moreover, the simple structure of a joint part is beneficial for the parametric representation of a hip joint. 2.2. Mechanism model of hip joint and thigh-femur Due to the stiffness of the aluminum alloy, the joint part is treated as a rigid body. Based on the theory of machinery, the part is abstractly illustrated as a link with a revolution joint, as shown in Fig. 3(a). In this figure, vector di is defined to expresses a link in a local coordinate frame (xi, yi, zi). From the joint part model (Fig. 2), it can be seen that the link is perpendicular to the lower plane and inclined by angle ai with respect to axis yi. Similarly, the thigh-femur can be regarded as a

Rotation axis

Inclination plane Upper part

Lower plane

Lower part

ai

ri ai

Half spherical shell

Upper plane

Fig. 2. Conceptual model of joint part.

Central plane

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3

yi Central plane

Rotation axis revolution joint

Thigh-femur link ai

Lower plane

Link

di

xi Upper plane

ri

Spherical joint (a)

(b)

Fig. 3. Mechanism modes of (a) hip joint and (b) thigh-femur.

link with a spherical joint because the bone has a certain stiffness, as illustrated in Fig. 3(b). Because the spherical joint has three degrees of freedom (DoF), it enables the thigh-femur link to rotate spatially. The coupling mechanism of the hip joint and the thigh-femur is firstly explained based on the above links, as shown in Fig. 4. It consists of five links, four revolution joints, a cylindrical joint, and a spherical joint. Links 1, 2, 3, 4 and 5 correspond to the four joint parts and thigh-femur, respectively. Variable θi is the relative rotation of link i. From view of relative motion, thigh-femur can rotate and translate with respect to joint part. Therefore, the cylindrical joint is designed to connect these two links. Especially, the cylindrical joint nullifies the impact between the hip joint and the thigh-femur. From Fig. 4(a), it can be seen that the cylindrical joint causes the thigh-femur to be perpendicular to the lower plane of Joint part 4 at all times. Among the five joint parts, Joint part 4 is the smallest in size. So long as the low plane diameter of Joint part 4 is bigger than human thigh, there is no impact between the thigh-femur and joint parts. Above all, the main characteristic of the coupling mechanism is that it represents the impact effect between the hip joint and the thigh-femur via the cylindrical joint. To realize the free rotation of Link 5, the coupling mechanism must have three degrees of freedom (DoF). Generally, a rigid link has six DoF in space. The revolution joint, cylindrical joint, and spherical joint possess 5, 4, and 3 constraints, respectively. From Fig. 4(b), coupling mechanism has 30 (=5 × 6) DoF and 27 (=4 × 5 + 4 + 3) constraints. Therefore, the coupling mechanism has a total of 3 (=30–27) DoF. Therefore, the proposed coupling mechanism enables free rotation in three-dimensional space.

global coordinate frame (x0, y0, z0), points K and S are expressed by vectors RK and RS respectively. Point S is the position of revolution joint 4. Since line KS is collinear to Link 4, vector RKS (=RS–RK) must be parallel to vector d4. This parallel relationship can be expressed as RKS ∥d4 ⇔RKS ¼ kd4 ⇔RK ¼ RS −kd4

ð1Þ

where d4 is the length vector of Link 4 and k is any positive real. Because vector RS equals the vector sum of Links 1, 2 and 3, RS ¼ d1 þ d2 þ d3

ð2Þ

Substituting Eq. (2) into Eq. (1) yields RK ¼ d1 þ d2 þ d3 −kd4 ¼ d1 þ d2 þ d3 þ sd4

ð3Þ

where s is any negative real. Based on Fig. 3(a), vectors d1, d2, d3 and d4 can be calculated by 2

3 2 3 − sina1 2  − sin2 α 3 Y 2 4 5 4 d3 ¼ r1 d1 ¼ r1 sina1 cosα j cosa1 sinα 3 cosα 3 5 j¼1 0 0 2 3 2 3 2 1  3  − sin2 α 2 − sin α4 Y Y 2  24 4 5 d2 ¼ r1 cosα j d4 ¼ r1 cosα j sinα 2 cosα 2 sinα 4 cosα 4 5 j¼1 j¼1 0 0

ð4Þ

2.3. Configuration of coupling mechanism

Since vectors di are expressed in a different coordinate frame (xi, yi, zi), they should be transformed into the global coordinate frame (x0, y0, z0). Through coordinate transformation, vectors di are rewritten as vectors Di in the global coordinate frame (x0, y0, z0).

In Fig. 4(b), the coupling mechanism is not unique, since the spherical joint may lie on any point, Kˊ, along line KS. Thus, the configuration of the mechanism needs to be discussed further. The main aim of this study is to derive position vector RK of point K. In the

D1 D2 D3 D4

¼ M1 d1 ¼ M1 T1 M2 d2 ¼ M1 T1 M2 T2 M3 d3 ¼ M1 T1 M2 T2 M3 T3 M4 d4

Fig. 4. (a) Assemble model and (b) coupling mechanism of hip joint and thigh-femur.

ð5Þ

4

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y Cylindrical joint

Human thigh (Link 5)

Link 4 θ4 Link 3 a3 Rotational joint 3

a4 Joint part 4 (Link 4)

Joint part 3 (Link 3)

θ3

Rotational joint 4

Joint part 2 (Link 2)

Rotational bearings (Rotational joint 4) Compound bearings (Compound joint) (a)

Link 5 θ1/θ2 z

Link 2 a2 Compound rotational joint

o

x Ground

(b)

Fig. 5. (a) Assemble model and (b) coupling mechanism of specific configuration.

where Mi and Ti describe the rotation and orientation from (xi, yi, zi) to (xi-1, yi-1, zi-1), respectively.

3. Analytical solution of coupling mechanism 3.1. Motion analysis of coupling mechanism

2 Mi ¼ 4

cosθi 0 ‐ sinθi

0 1 0

3 sinθi 0 5 cosθi

2 cosα i Ti ¼ 4 sinα i 0

− sinα i cosα i 0

3 0 05 1

ð6Þ

By substituting Eqs. (4) and (6) into Eq. (5), RK can be written as R K ¼ d1 þ d2 þ d3 þ sd4 ¼ D1 þ D2 þ D3 þ sD4 ⇔RK ¼ M1 fd1 þ T1 M2 ½d2 þ T2 M3 ðd3 þ sT3 M4 d4 Þg

ð7Þ

Eq. (7) can solve two basic problems. If r1, a1, a2, a3 and a4 are known, RK is a function of θ1, θ2, θ3 and θ4. Thus, the envelop of a spherical joint can be obtained by calculating RK. This can help designers to estimate the parameters of the hip joint and improve its design. This problem, however, will not be discussed in this paper. The second problem is the motion of the mechanism. The aim here is to derive equations of motion of the joint parts. As is apparent, Eq. (7) has five variables, θ1, θ2, θ3, θ4 and s, under the condition that r1, a1, a2, a3, a4 and RK are known. Since any two variables are independent, the rest of the three variables can be expressed by those independent variables. For example, if θ1 and θ2 are independent variables, then θ3, θ4 and s can be expressed as functions of θ1 and θ2. Most of mechanism's configurations have no analytic solution. However, some specific configurations are beneficial to the design and analysis. Based on Fig. 4(b), three constraints are enforced to determine a specific configuration, 8 < d1 ¼ 0 a ¼0 : 1 RK ¼ 0

As far as motion analysis is concerned, Link 5 is considered an active component and other links are driven components. As shown in Fig. 5 (b), Link 5 rotates around the origin o and forces Links 2, 3 and 4 to rotate relatively. Obviously, motion analysis involves establishing equations of θ2, θ3 and θ4 under the constraint of a fixed-point rotation. Kinematics shows that the fixed-point rotation can be discomposed into fixed-axis rotation and planar rotation. If Links 2, 3 and 4 are connected, the specific mechanism will perform fixed-point rotation, and no relative rotation occurs. It can be concluded that fixed-point rotation cannot cause the links' relative rotation. In addition, θ4 can be calculated because Link 4 coincides with Link 5. Above all, the main aim of this section is to solve θ2 and θ3 in the state of planar rotation. Although solving Eq. (7) can directly give θ2 and θ3, it cannot explicitly describe any more details. Therefore, a vector graphic method is proposed to analyze the planar rotation, as shown in Fig. 6. In this figure, the line segments OA, AS, and OS represent links 2, 3 and 5, respectively. Theoretically, line-segment OA performs rotation around axis y0 and line-segment AS is rotation around OA. According to mechanism kinematic, above fixed-axis rotations provide two degree of freedom totally. It equals to the degree of freedom of planar rotation. Namely, both fixed-axis rotations enable to synthesize planar rotation of OS. But, this paper concerns to decompose planar rotation into two fixed-axis rotations. In coordinate plane xz, curve C1 is trajectory projection of point S. View T displays trajectory C2 of point S in local _

coordinate frame xayaza. Arc SC is planar trajectory of point B around the origin O, which is with the range of [−ad, ad]. Initially, θ2 = θ3 = 0 and line OS does not rotate. At any given moment, let us assume that OS rotates to OP through degree a. Then,

ð8Þ

where the first two constraints (d1 = 0 and a1 = 0) cause revolution joints 1 and 2 to combine into a compound revolution joint. The third constraint (RK = 0) means that the spherical joint is moved to the origin o. Consequently, the proposed coupling mechanism becomes a specific mechanism, as shown in Fig. 5(b). The main feature of the specific mechanism is its compound revolution joint, which helps obtain an analytical solution for the mechanism's motion. Although numerical computation is commonly applied in engineering fields, analytical solutions are more accurate and efficient than the numerical method. There are other mechanisms for a different set of constraints. For example, d4 = 0, a4 = 0 and RK = 0. These mechanisms, however, will not be discussed here.

Fig. 6. Schematic diagrams of planar rotation decomposition.

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from point P, a horizontal line segment, PPM is drawn. Point PM lies on line segment SC. Then, a vertical line segment PMQ is drawn to intersect with curve C1. The inclination of line-segment OQ equals θ2. Similarly, vertical line segment PM Pˊ is drawn to intersect with trajectory C4 in View T. The inclination of line segment Pˊoa equals θ3. To reach line segment OP, line segments AS and OA must rotate. First, AS rotates around a stationary OA through θ3 (θ2 = 0). Thus, point S moves to point Pˊ along C2. Then, both line segments together rotate θ2 around axis, y0. It means that point Q rotates to point F around the origin O in the coordinate plane x0z0, where point F is a projection of point P. As a result, point S moves from Pˊ to point P. 3.2. Derivation of θ2 and θ3 In Fig. 6, the position of point P is also expressed as (r, β, γ) in a spherical coordinate frame. Since both β and γ are related to thighfemur motion, the main aim is to derive θ2 and θ3 as a function of β and γ. It is obvious that β originates from the abduction of human thigh directly. Therefore, β will be neglected for deriving motion equation. On the contrary, γ is related to planar motion of thighfemur. As mentioned earlier, r1, a1, a2, a3, a4 and ad are already known. According to Eq. (4), vector length di can be calculated as: 8 < d2 ¼ r 1 sinα 2 d ¼ r 1 cosα 2 sinα 3 : 3 d4 ¼ r 1 cosα 2 cosα 3 sinα 4

5

In coordinate plane x0y0z0, position vector PQ of point Q equals 2

3 0 4 PQ ¼ −dOQ cosθ2 5 −dOQ sinθ2

ð13Þ

Moreover, position vector Pw of point Pˊ can be expressed as PW ¼ MP0 þ t

ð14Þ

where M and t are the respective transformation matrix and displacement vector from coordinate frame xayaza to x0y0z0, and Pˊ is the position vector of point Pˊ in coordinate frame xayaza. 2 3 2 3 cosα 2 − sinα 2 0 −ðd2 þ d3 cosα 3 Þ sinα 2 M ¼ 4 sinα 2 cosα 2 0 5 t ¼ 4 ðd2 þ d3 cosα 3 Þ cosα 2 5 0 0 1 0 2 3 −d3 sinα 3 cosθ3 5 P0 ¼4 0 −d3 sinα 3 sinθ3 Because point Q is the projection of point Pˊ, the coordinates of PQ and PW are equal in coordinate plane x0z0. Namely, 

dOQ cosθ2 dOQ sinθ2



 ¼

d3 cosα 2 sinα 3 cosδ þ ðd2 þ d3 cosα 3 Þ sinα 2 d3 sinα 3 sinθ3

 ð15Þ

ð9Þ By solving Eq. (15), θ2 and θ3 can be obtained. qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 3 2 2  d3 sinα 3 − ðd3 sinα 3 Þ − dOQ sinα 2 6 7   6 7 sinα dOQ q cosθ2 6 7 2 tanα 2 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ¼6 7 ð16Þ   cosθ3 6 d sinα ð cosα Þ2 − ðd sinα Þ2 − d sinα 2 7 3 2 3 3 OQ 2 4 3 5 2

Since points P and PM have the same coordinate, y, Eq. (10) can be written as

αy ¼ αd

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 d2 þ d3 þ 2d2 d3 cosðα 3 Þ cosðα d −aÞ−d2 cosα 2 −d3 cosðα 2 þ α 3 Þ

ð10Þ where ay is the inclination of line OPM. In coordinate plane x0–y0, position vector PM of point PM is expressed as   αy αy PB þ PC PM ¼ 1− ad ad



where θ2 N 0 and θ3 N 0. Eq. (16) gives θ2 and θ3 as a function of a. Therefore, a needs to be discussed further. From Section 3.1, it can be concluded that a is only related to γ. Based on Fig. 6, a can be obtained as α ¼ α d −γ

3.3. Calculation of a2 and a3

−d2 sinα 2 −d3 sinðα 2 þ α 3 Þ d2 cosα 2 þ d3 cosðα 2 þ α 3 Þ



 PC ¼

0 d2 cosα 2 þ d3 cosðα 3 −α 2 Þ



From Fig. 6, it can be seen that point C lies on the coordinate axis y0. By applying the sine theorem to △OAC, d3 can be expressed in terms of d2 as d3 ¼

According to |OQ| = |OF|, length dOQ of line segment OQ can be obtained as  dOQ ¼

ð17Þ

ð11Þ

where PB and PC are position vectors of points P and C. Then, PB ¼

d3 sinα 3 ð sinα 2 Þ2

d3 ½ cosðα 3 −α 2 Þ− cosðα 2 þ α 3 Þ

 α d −α y ½d2 sinα 2 þ d3 sinðα 2 þ α 3 Þ αd

ð12Þ

sinα 2 d2 sinðα 3 −α 2 Þ

ð18Þ

Substituting Eq. (9) into Eq. (18), the relationship between α2 and α3 can be obtained as: ð sinα 3 Þ2 − tanα 2 sinα 3 cosα 3 ¼ ð tanα 2 Þ2

Eq. (10) Orientation of thigh Eq. (17) a ay γ Known r1 Known ad

Eq. (21)

a2

Eq. (20)

a3

Eq. (12) Eq. (22)

Fig. 7. Hip-joint motion calculation procedure.

dOQ α4

Eq. (16)

θ2, θ3

ð19Þ

6

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(rad)

θ2=30 θ3=58

Thigh-femur bar

θ3 Joint part 3

Angle θ and θ3

θ2=60 θ3=116 θ2

angle a

Joint part 2

Marks

(rad)

(a)

(b)

Fig. 8. Illustrations of (a) the curves of angles θ2 and θ3 and (b) the joint prototype.

Through further calculation, Eq. (19) can be rewritten as: qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 þ 5−4ð tanα 2 Þ2 h i tanα 2 tanα 3 ¼ 2 1−ð tanα 2 Þ2

ð20Þ

From Fig. 6, it can be seen that ∠AOS equals ∠AOC. Thus, α2 can be expressed as Eq. (21). α2 ¼

αd 2

ð21Þ

Based on a2 and a3, a4 can be obtained and shown as following equation. α 4 ¼ α 3 −α 2

ð22Þ

Above all, the hip joint can be completely constructed under the conditions of r1 and ad, and the hip joint motion can be calculated for any orientation γ of the thigh-femur. For ease of understanding, the calculation procedure is illustrated in Fig. 7. 4. Case study A case study is conducted under the condition that r1 = 226 mm, ad = 88°and β = 180 .̊ The calculation results are plotted in Fig. 8(a). In this figure, both the curves θ2 and θ3 are smooth and continuous. This proves that the established equations are correct. To verify the

(1) θ2=0 θ3=0

and

(2) θ2=30

and θ3=58

practical application of the hip joint, a prototype was manufactured based on the proposed coupling mechanism, as shown in Fig. 8(b). In this figure, joint parts 3 and 4 are fixed together due to zero relative rotation. The thigh-femur part was manufactured as a bar, to save raw material. In order to measure relative rotation between joint parts, some marking lines were drawn on joint parts 2 and 3. Angular interval between marking lines is set to 30°. The experimental results are partly shown in Fig. 9, and reveal that the thigh-femur bar can assume any spatial orientation. Because of motion continuity of joint parts, four rotational statuses are illustrated to represent relative rotation. Related experiment results are also shown in Fig. 8(a). Due to this agreement between theory and experiment, it can be concluded that the proposed coupling model is reasonable. 5. Conclusions The core objective of this paper is to construct a coupling mechanism model of the hard hip joint with the thigh-femur, and derive its analytical solution. The new mechanism will benefit space agencies by enabling them to develop advanced spacesuit hip-joint designs. Firstly, a conceptual model of the hard hip joint is discussed in detail. The joint parts are regarded as links due to their material rigidity. By connecting all the links, a coupling mechanism is formed to represent the conceptual model. It includes five links and six different joints. Especially, a cylindrical joint is adopted to avoid any impact between the hip joint and the thigh-femur. Secondly, three constraints are enforced to construct a specific mechanism from the coupling mechanism. Its main feature is a compound revolute joint, which

(3) θ2=60

Fig. 9. Experiment results.

and θ3=112

(4) θ2=90

and θ3=180

W. Zhen-Wei et al. / Materials and Design 187 (2020) 108321

reduces one link. The feature helps derive the analytical solution of the mechanism's motion. Based on the specific mechanism, a graphic method is proposed to perform motion decomposition of the coupling mechanism. It explicitly describes the decomposition principle of joint rotation. Consequently, the equations of motion of the joint parts as well as the structural parameters are obtained. Finally, a case study confirmed the working of the coupling mechanism and equations of motion. It should be noted that the coupling mechanism model is proposed base on the condition that all bearings are neglected. Strictly speaking, they affect the accuracy of modeling and computation to some extent. Moreover, dead point of coupling mechanism should be analyzed furtherly so as to realize smooth rotation. CRediT authorship contribution statement Wang Zhen-Wei: Investigation. Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgments This study was funded by The National Natural Science Foundation of China (grant number 51675087). References [1] P.J. Bertrand, A. Anderson, A. Hilbert, D. Newman, Feasibility of spacesuit kinematics and human-suit interactions, 44th ICES, 13–17 July 2014 2014. [2] J. Hochstein, Astronaut Total Injury Database and Finger/Hand Injuries during EVA Training and Tasks, International Space University, M. S. Strasbourg, FR, 2008. [3] P. Schmidt, An Investigation of Space Suit Mobility With Applications to EVA Operations, PhD. Cambridge Massachusetts Institute of Technology, MA, 2001. [4] M.G. Lewis, The effect of accounting for biarticularity in hip flexor and hip extensor joint torque representations, Hum. Mov. Sci. 57 (2018) 388–399.

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