#### Abstract

Spacesuit hip joint plays an important role on astronaut activities, such as planetary walking and surveying. This paper proposes a conceptual design of hard hip joint in consideration of the coupling effect of spacesuit hip joint and astronaut thigh. Firstly, lower extremity activities are introduced to illustrate the mobility of hard hip joint, such as walking, kneeing, and abduction. A conceptual design of hard hip joint is explained in detail, including geometric structure, components, design parameters, and mechanism models. Secondly, a 3-linkage coupling mechanism model is built up by synthesizing that conceptual design of hard hip joint. An equiangular dual-perpendicular representation method is brought out to parameterize that mechanism model of hard hip joint. Particularly, four geometric constraints are, respectively, given out to avoid impact between the hip joint and the thigh and to ensure the continuity of thigh motion. Finally, motion equations of hip joint parts are established by using coordinate transformation and vector representation. A case study is conducted to verify the correctness of the proposed representation method and that coupling mechanism model.

#### 1. Introduction

Hip joint is an important component in spacesuit, which enables mobility of astronauts wearing pressurized spacesuits to complete missions, including walking and surveying. Hip joint is briefly classified into soft hip joint and hard hip joint. Generally, hard hip joint is made of some rigid materials, such as aluminum alloy and stiffness composite. Soft hip joint is made of soft materials, such as nylon and fabric. General spacesuit is pressurized with gas to a certain pressure level making it stiff in the vacuum of space [1]. For soft hip joint, the stiffen spacesuit greatly increase unnecessary energy expenditure and impeded mobility. Additional factors also include change in suit column and fabric stiffness as the joints bend [2]. Relatively, hard hip joint can avoid above problems because deformation of rigid material caused by pressurized gas is very little. The major advantage of hard joint is that torque moment derived by bearing friction is less than other kinds of hip joint. Therefore, hard hip joint has been widely applied to some spacesuits, such as the *Z* series spacesuit [3] and Mark III spacesuit [4]. On the other hand, the primary problem of hard joint is that the placement of bearings causes programming and potentially unnatural movement and stances. Presently, it is one of technical bottlenecks.

Spacesuit field involves many topics widely, such as mobility and agility [5], human-suit interaction [6], astronaut injury estimation [7], joint torque testing [8], human movements [9, 10], and gait simulation [11, 12]. Among those topics, hip joint mobility is one of the basic research focuses. Around joint mobility, many kinds of spacesuit joint had been developed, including flat-pattern joint, bellow-type joint, and rotation-bearing joint. Now, there are many research achievements in motion analysis and test [13, 14], computational methods [15, 16], human factors [17, 18], and joint development [19, 20]. As far as joint design is concerned, there is relatively less research on the improvement of hard joint design for many years. With the development of planetary explorations, a new spacesuit design is becoming more important, such as Mars exploration and lunar landing.

Spacesuit is different from other classical spacecraft, which is characterized as the human-suit interactive spacecraft. As for spacesuit hip joint, there exists a strong coupling effect between hip joint and astronaut thigh. The coupling effect is embodied by impact, rubbing, etc. Therefore, the conceptual design of hip joint should pay attention to above coupling effect. To solve above problem, this paper brings forward an equiangular dual-perpendicular representation method and two related geometric constraints. Moreover, a 3-linkage coupling mechanism model is constructed based on a conceptual model of the hip joint. That coupling mechanism model is helpful for parametric design and motion analysis. To ensure the motion continuity of the joint and thigh, two additional geometric constraints are brought out and discussed in detail. Furthermore, motion equations of hip joint part are established using coordinate transformation and vector representation. Finally, a case study is conducted to verify the correctness of the proposed representation method and coupling mechanism model of the hip joint.

#### 2. Conceptual Design of Hard Hip Joint

##### 2.1. Conceptual Model of Hip Joint

Four basic lower extremity activities of designed spacesuit are illustrated in Figure 1, including standing, walking, kneeing, and abduction. Those activities require the hip joint to be mobile and flexible. Although four activities appear different, they can be generalized as hip joint motion based on kinematics. Namely, every activity corresponds to specific rotation of the hip joint, but their rotational angles are different from each other. Also, Figure 1 shows some joints and components in designed spacesuit. This paper only discusses the hip joint, where it is made of aluminum alloy and designed to connect the waist part with the thigh part. When a suited astronaut moves the thigh, related hip joint will be driven to move synchronously. Thus, low extremity activities can be performed. Around the hip joint, the following sections will discuss its components, geometric structure, and design parameters.

Conceptual models of the hip joint and its components are constructed, as shown in Figure 2. From a view of mechanism design, the hip joint can be regarded as a rigid assembly with 3 degrees-of-freedom, where the hip joint consists of briefs part, right hip joint, left hip joint, and rotation bearings. Bearings are not displayed due to no effect on conceptual design. The structure of left and right hip joint is designed to be the same. It is composed of two parts—upper part and lower part. Both parts are connected together by a rotation bearing. Similarly, briefs part is, respectively, connected with two hip joint parts by rotation bearings. Due to rotation bearings, low part and high part can rotate independently. In other words, thigh motion can be decomposed into relative rotations of upper and lower parts. That is the basic thought for the conceptual design of the hip joint.

##### 2.2. Geometric Structure of Hip Joint Part

To reduce manufacturing cost, a similar geometric structure is used to design upper part and lower part, as shown in Figure 3. As a whole, it is a shell body with uniform thickness of 5 mm. With neglect of thickness, the geometric structure is formed by two tangent circles with inclined angle and one ruled surface sweeping from upper circle to lower circle. Where is the tangent point of two circles, and are the corresponding center point of lower circle and upper circle. Through those three points, a central plane is constructed to parameterize joint part. Moreover, a local coordinate frame is also established to express the geometric shape of joint part. In a central plane, the geometric structure can be represented by parameters , , and completely, where and are the radius of upper circle and lower circle, respectively. Subscript is the index of joint part, i.e., or 2, and number 1 stands for upper part. These parameters are determined according to design requirements.

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Due to large stiffness, hip joint part is treated as a rigid body theoretically. Thus, the geometric structure can be synthesized to be one link from point to point based on the mechanism theory. Moreover, a rotation joint is placed at point to connect other joint part. Generally, link is not required to be perpendicular to two circles. On the contrary, rotation joint must be vertical to lower circle to ensure relative rotation of hip joint part. As a result, upper and lower parts can be, respectively, represented as links and parameterized by sets {, , and } and {, , and }. Considering rigidity of human bone, we also simplify thigh as one link with a spherical joint. Although this simplification causes error, it is helpful for analytical solution of joint motion. Above all, joint parts and thigh can be regarded as link under a condition of enough stiffness.

##### 2.3. Coupling Mechanism of Hip Joint Assembly

By combining the thigh with the hip joint, a hip joint assembly is constructed, as shown in Figure 4(a). It consists of astronaut torso, thigh, briefs part, and hip joint. Generally, spacesuit mounted on astronaut should be by internal textile belt. A fixed belt in the waist joint is used to restrict lateral location. Thus, briefs part location is deterministic related to astronaut. The location limit is not our research objective. We do not discuss it anymore.

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By assembling above links, a 3-linkage coupling mechanism model of hip joint assembly can be built up, as shown in Figure 4(b). It consists of three links, one cylindrical joint, two rotation joints, and ground base, where links 1, 2, and 3 correspond to upper part, lower part, and thigh, respectively. Astronaut torso is modeled as ground base. Link 1 connects with ground base by rotation joint 1 and with link 2 by rotation joint 2. Relative rotation of link 1 and link 2 can be measured by angles and . Particularly, link 3 is connected with link 2 by cylindrical joint and with ground base by spherical joint. In order to ensure motion consistency between human thigh and hip joint, link 3 needs to be located at original point . In other words, spherical joint and rotational joint 1 are coincident to original point *.* All links are measured and expressed in reference coordinate frame . More details about coordinate frame will be discussed in Section 3.2.

#### 3. Parameter Calculation of Hip Joint

##### 3.1. Parameterization of Hip Joint

Generally, there are many requirements on spacesuit, such as motion, safety, strength, and weight. This paper is mainly aimed at impacting and motioning continuity. To solve above two problems, an equiangular dual-perpendicular method is firstly brought out to parameterize a conceptual model of hard hip joint, as illustrated in Figure 5, where upper part and lower part are aligned with their central planes. Initial angles of two joint parts equal to zero, , where links 1, 2, and 3 are represented by segment lines *JC*, *CE*, and *JE*, respectively. It can be seen that lengths of segment lines *PJ*, *PC*, and *PE* are equal to radiuses , , and , respectively. Next, we will introduce four geometric constraints in order to avoid impact and ensure motion continuity.

To avoid impact between the hip joint and the thigh, two geometric constraints must be satisfied. The first constraint is that both segment lines *JE* and *JC* are, respectively, perpendicular to segment lines *PE* and *PC*. The second constraint is that segment line *PC* is a diagonal line of angle ∠*JPE*. It can be concluded that above constraints enable segment line *JE* to be perpendicular to the lower circle of lower part all the time. In other words, impact will not happen between the hip joint and the thigh. Moreover, above two constraints cause inclined angle to be equal to inclined angle , .

In order to ensure continuous motion of the thigh, two geometric constraints are proposed in addition. The first constraint is that segment line *CE* and *CD* is symmetric about segment line *CJ*. The second constraint is that point must lie in coordinate axis . Under condition of above two constraints, motion continuity means that segment line *JE* can rotate around point freely. Namely, segment line *JE* is a fixed point rotation. According to kinematics, rotation around fixed point can be discomposed into a planar rotation around point and a rotation around coordinate axis . Obviously, the latter rotation is continuous. So, main difficulty is how to realize the continuity of planar rotation. As mentioned above, two additional constraints enable segment line *JE* to rotate along planar arc . As a result, motion continuity is realizable according to above geometric constraint.

Above all, those problems can be solved by introducing four geometric constraints, including two perpendicular constraints, one symmetric constraint and one coincident constraint.

Based on above four constraints, structure parameters of hip joint and briefs part can be obtained. Next, we derive the structure parameters of hip joint. In Figure 5, parameters are determined by design requirement and parameter is given as the angle limit of thigh motion. Both parameters are known. Through geometric analysis, it is concluded that parameters and can represent the geometric structure of hip joint completely. Thus, the main work is to calculate points and . In a reference coordinate system , coordinates of points and can be obtained by using vector representation, as shown as equation (1), where trigonometric functions *cosine*() and *sine*() are, respectively, abbreviated as letters and . For example, . Both abbreviated letters and will be used in following equations.

##### 3.2. Parameterization of Briefs Part

Intuitively, the geometric structure of briefs part is a spherical shell. Neglecting its shell thickness, it consists of three tangent circles, as shown in Figure 6. Those circles correspond to connecting interfaces with waist part, left hip joint, and right hip joint, respectively. Points , , and are tangent points. Moreover, two global coordinate frames *XYZ* and *X**Y**Z* are, respectively, established in the center points of waist part and spherical shell. Left and right circles are designed to have the same inclined angle . Also, a reference coordinate frame *xyz* is established by three points , , and . Angle between coordinate planes *YZ* and *yz* is measured by parameter . From Figure 6, it can be seen that structure parameters of briefs part include the radius of spherical shell and two angle parameters and .

Among above three parameters, parameters and are known because they can be determined by design requirements. Therefore, two radiuses and are needed to be calculated, where parameter is the radius of the waist part. From View A-A in Figure 6, radius can be obtained, as shown as

In global coordinate frame *X**Y**Z*, position vector of any point in the left circle of briefs part can be obtained by vector algebra, as shown as
where parameter is the rotation angle of point about coordinate axis . According to tangent constraint between waist circle and left circle, angle can be obtained by coordinate transformation, as shown as

By combining equations (3) and (4), position vector of any point in global coordinate frame *X**Y**Z* can be rewritten as

Furthermore, radius can be calculated by using coordinates and of vector , as shown as

From equations (1) and (5), it can be seen that parameters of hip joint and briefs part are analytically calculated under the condition of given parameters , , , and . It is known that expressing a vector in different coordinate frame may bring more convenience for calculation. This paper derives translation vector and transformation matrix between coordinate frames *xyz* and *XYZ*, where parameter is the position vector of center point in reference coordinate frame *xyz* and parameter is a transformation matrix between coordinate frames *xyz* and *XYZ*. Through geometric analysis, both parameters and are shown as

#### 4. Motion Equations of Hip Joint

##### 4.1. Coupling Mechanism Model of Hip Joint Assembly

Firstly, we try to construct the coupling mechanism model of hip joint assembly in global coordinate frame *XYZ*. In equations (1), (3), and (5), those vectors are derived in reference coordinate frame *xyz*. However, many gait experiments measure thigh motion in coordinate frame *XYZ*. To establish motion equation correctly, we must represent hip joint assembly in coordinate frame *XYZ*. By assembling hip joint with briefs part, a global coupling mechanism model is constructed in coordinate frame *XYZ*, as shown in Figure 7(b). It looks like a four-linkage mechanism, where briefs part is regarded as a link from origin point to center point . Briefs link is fixed in coordinate frame *XYZ*. To express thigh motion, we define unit vector to represent link 3 in global coordinate frame *XYZ*, as shown in Figure 7(a), where link 3 is measured by angle parameters and . Similarly, two parameters and represent relative rotation of link 2 and link 1, respectively.

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##### 4.2. Motion Equations of Hip Joints

Next, we will derive motion equations of upper part (link 1) and lower part (link 2) in coordinate frame *xyz*. More details are shown in Figure 5, where unit vector is illustrated to represent segment line *JE*. Obviously, it can be measured by two parameters and . For a given angle , segment line *JE* moves to segment line *JG*. From point , a parallel line *GH* is drawn to intersect line *ED* at point . Point is the projection of point in coordinate plane *x*_{1}*y*_{1}. Then, circle is formed through point . From point , vertical line *HM* intersects with circle at points and . It is concluded that rotation of upper part can be measured by parameter . In View A, motion trajectory of lower part can be expressed by circle . Then, vertical line *HK* is drawn to intersect with circle at point . Relative rotation of lower part can be calculated by parameter .

From circle , it can be seen that length of line equals to length of line . In coordinate frame *xyz*, coordinates of points and can be obtained in a form of vectors and , as shown as

Because of , parameters and can be derived, as shown as

Secondly, we will derive thigh motion equation in coordinate frame *xyz*. In Figure 7, unit vector can be written as equation (10) in coordinate frame *XYZ*.

By coordinate transformation, unit vector can be expressed as vector in coordinate frame *xyz*, as shown as

By substituting equations (7) and (10) into equation (11), vector can be rewritten as

From Figure 5, it can be seen that vector can also be written as vector in a form of parameters and .

According to , parameters and can be calculated by

Based on the relationship between planar rotation and fixed axis rotation, parameters and can be derived in coordinate frame *XYZ*, as shown as

Above all, motion equations (equation (15)) of lower part and upper part have been established analytically. Of course, thigh status (, ) can be calculated under condition of given ration angles (, ) of hip joint.

For convenience of programming, computation procedure is given to solve design parameters and motion equations based on known conditions, as shown in Figure 8, where parameters , , , and are known as mentioned before. Parameters , , and *r _{w}*, respectively, represent the geometric structure of hip joint parts and briefs part. Parameters and are the rotation angle of upper part and lower part. Parameters and express thigh motion, which are input for equation (15). Firstly, we determine parameters , , , and according to design requirement. Then, using equations (10) and (15) solve hip joint motion for any given thigh parameters. Finally, structural parameters are calculated by equations (1) and (6).

##### 4.3. A Case Study

Based on above computation procedure, related program was developed to carry out a case study, where design parameters are set to , , , and . Thigh data had been downloaded from the website [21]. Only flexion/extension data are adopted. According to above computation procedure, motion equations of hip joint can be computed and plotted in Figure 9. It can be seen that both curves of parameters and are smooth and continuous. They are consistent with theoretical expect. Above all, our proposed representation method and coupling model are correct and feasible.

#### 5. Conclusion

Around a coupling effect of hip joint and thigh, this paper proposes an equiangular dual-perpendicular method to design a conceptual model of hip joint. Geometric structure and coupling constraints are discussed in detail. Specifically speaking, two perpendicular constraints are given out to avoid impact between hip joint and thigh. Symmetric and coincident constraints are brought out to realize thigh continuous motion. Based on above constraints, a 3-linkage coupling mechanism model is built up. Motion equations of hip joint are derived by using coordinate transformation and vector representation. Meanwhile, related computation procedure is formed to solve structural parameters and motion parameters, respectively. Finally, a case study is conducted to verify the proposed representation method and motion equations. Results show that the conceptual design of hip joint is correct and feasible.

#### Data Availability

No data were used to support this study.

#### Conflicts of Interest

The authors declare that they have no conflicts of interest.

#### Acknowledgments

The National Natural Science Foundation of China under the grant No. 51675087 supports this research.