Design, analysis of self-configurable modular adjustable latch lock for segmented space mirrors

Xupeng Li; Wei Wang; Jinfeng Shi; Chenchen Wang; Hui Zhao; Xuewu Fan

doi:10.1364/OE.26.018064

1. Introduction

For decades, demand for higher optical resolution and larger aperture of primary mirror (PM) has driven the aerospace observatory moving forward to advance our most compelling themes such as ‘life in the universe’. Traditional space optical telescopes employing monolithic mirrors are increasingly difficult to satisfy optical requirements and shorten manufacturing cycles. The next generation of large ultraviolet-optical-infrared (UVOIR) space telescope with the segmented PM [1] will utilize several small modular mirrors to form one large mirror. As an IR-optimized successor to Hubble Space Telescope [2], James Webb Space Telescope (JWST) [3] has become the flagship of future large on-orbit deployable camera. JWST has eighteen 1.32 m flat-to-flat hex shaped mirrors called modular space primary mirror assembly (PMA), which are mounted on a three-section backplane structure [4]. Two deployable wing-structures allow the PM with 6.5 m diameter stowed into a 5.5 m launch vehicle fairing size [5]. However, looking beyond JWST, there has been a proposal that observatories with both PMA and supporting structures modularized [6–9] will enable space telescope components to be launched incrementally, so that future space mirrors will overcome launching volume and mass limitations. In this case, a connection mechanism for autonomous precise self-assembly should be developed to aggregate PMAs on orbit.

The docking mechanisms aiming at autonomous rendezvous and self-assembly of small-scale robots have been investigated by several research groups [10–13]. The Autonomous Satellite Docking System (ASDS) utilized the soft-docking technology to minimize the impact during capture [14–16]. The Engineering Test Satellite VII (ETS-VII) led by Japanese research group tested and demonstrated automatic rendezvous and docking capability in space [17]. The Synchronized Position Hold Engage Reorient Experimental Satellites (SPHERES) team [18] developed Universal Docking Port (UDP) [19] to mature the crucial technologies including routine formation flight, dock/undock and maneuvering operation [20–22], which provides two counter-rotating disks to interconnect two satellites rigidly. However, the connection mechanism using for modular PMA requires compact and multifunctional design to face many challenges, such as effective capture, optical alignment and robust locking abilities.

The future self-reconfigurable PMA design is defined as one that consists of various standardized components [23]. Specifically, it is a kind of composition including many separate modules with multiple use for space-based functions, such as actuated hybrid mirror segments, rigid and flexible support structures and electronics & metrology equipment. The addition of Self-configurable Modular Adjustable Latch Lock (SMALL) is a critical conceptual upgrade to prospective PMA. One benefit of SMALL is that with the ability to dock/undock, re-orient and adjust, this simple and compact design provides a chance for segmented mirrors to function monolithically with the on-orbit connection available through the explicit interface. Furthermore, universal design appearance can endow the next generation of large space telescope with the ability to be launched by stacking multiple modules within one or more launching vehicles. After reaching the designated orbit, the modules could be deployed and assembled by autonomous telerobotics or human-in-the-loop assistance. The assembled PM could then be reconfigured and re-phased to accommodate relevant optical mission requirements just like a conventional paradigm does. Another benefit of SMALL is that intrinsically tolerant to imperfections during ground manufacturing, assembly in 1g and launch will be improved in the optical chain with the addition of adjustable function. Moreover, the difficulty of maintenance could be alleviated by replacing particular sub-components instead of the entire equipment, so that the cost curve can be redefined and risks can be lowered substantially.

This paper is organized as follows. Section 2 addresses general design requirements of the connection mechanism for modular assembled mirrors and introduces the operation principle of SMALL in detail. In Section 3, the capture conditions of SMALL are analyzed, including the determination of the collision point location and the limitations on initial incident velocity. Section 4 investigates the latch-locking design and construction. In Section 5, simulation results are reported aiming at the contact performance between SMALLs. Also, the optical performance of two adjacent PMAs is discussed in the presence of gap errors. Section 6 concludes our statements and outlooks a brief prospect of future work.

2. Design requirements and operation principle

Considering the particularity of the mechanism connecting the segmented optical components and the repeatability of a number of space assembly tasks, the connection mechanism must satisfy the following four key requirements.

(1) Power efficiency: in order to improve assembly efficiency, energy requirements must be minimized on a large cluster of PMAs processing.
(2) Universality: as part of the modular components, each connection mechanism attached to PMA needs to be identical to each other in design and fabrication.
(3) Positioning and locking: to compensate for alignment errors, positioning misalignment can be automatically corrected to secure a reliable and accurate connection.
(4) dock/undock: with the telerobotical assistance or human intervention, the mechanism should have the ability to perform simple docking/undocking maneuvers.

The SMALL fully satisfies the requirements mentioned above. Some of the key features of SMALL are illustrated in Fig. 1. This connection mechanism includes: (a) a chamfered entrance hole and a grooved protruding pin which increase the docking range. (b) A positioning channel to limit five degrees of freedom (DOFs) to correct alignment error. (c) A latch lock to strengthen the combination of the two adjacent modules. (d) A linear actuator to adjust the interval of the joint parts. The key specifications of the design are summarized in Table 1.

Fig. 1 Design scheme of SMALL.

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Table 1. Key specifications of SMALL

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SMALL adopts mechanical interlocking rather than electromagnet drive to work in passive mode during most of functional period. Moreover, the characteristics of androgyny avoid master-slave structure design scheme to reduce the cost and shorten the manufacturing cycle. The design scheme of PMA is shown in Fig. 2. The interface of SMALL is attached to the outer wall of the PMA base, which provides an explicit and stable way to connect another module.

Fig. 2 SMALL within one PMA.

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The operation principle of SMALL is explained as follows.

(1) Capture stage: Using fiducial target tracing via benchmarking cameras, a pair of SMALLs are simultaneously close to each other till grooved pins make contact with the opposing entrance holes as shown in Fig. 3(a). The capture can be implemented with the relative attitude calculation and rational incident velocity estimation.
(2) Positioning stage: The pins enter the positioning channels whose function is to limit five DOFs of the whole connection combination except one along with axis direction of the channels. The androgyny design prevents possible misalignment errors (yaw, roll and offset) to the greatest extent as shown in Fig. 3(b).
(3) Locking & adjustment stage: The pins reach the top of locking mechanisms and start to push the flexible locking teeth to expand outward. The ferrules continue to move down along the outer wall of the teeth. During this period, the springs attached to the ferrules keep accumulating compressed energy. When the locking teeth engage with the insertion groove, locking teeth rebound as well as springs release energy so that the ferrule can clamp the locking teeth close to the top of locking mechanism as shown in Fig. 3(c). Once assembled, the gap between the pair of docking mirror segments is aligned to considerable mechanical error ranges, with the assistance of external metrology instruments and the internal actuators of SMALLs.
(4) Separation stage: If unpredictable incidents happen such as docking improperly or irreparable collisions occurring, this stage will be executed. The semi-rigid stick within the grooved pin extends out driven by the linear motor, pushing the guide plug to slide down the inner wall of the teeth. Because the plug and ferrule are glued, the ferrule moves down to alleviate the locking effect. On account of the special root structure of the locking teeth, the guide plug will push the locking teeth outwards and promote the separation of the two connection mechanisms as shown in Fig. 3(d).

Fig. 3 Operation stage of SMALL: (a) capture, (b) positioning, (c) locking & adjustment, (d) separation.

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The implementation of the complete connection mainly depends on the capture and locking stage. In section 3, contact analysis in capture stage will be investigated, including the determination of contact positions and the rational condition of incident velocities.

3. Contact analysis in capture stage

There are two types of failure collision, ineffective and viscous collision, which mainly occur in capture stage after the first contact between the pin and the inner wall of the hole. Ineffective collision means an inverted movement takes place, or the pin head collides repeatedly in the tapered hole. Viscous collision means the pin head stops moving forwards to the bottom of the opposing chamfered hole. In following section, the kinematic double-contact model is set up to obtain the docking initial conditions based on the androgynous characteristic. To avoid these two failure collision, the relationship between incident velocity and angle is investigated.

3.1 Initial capture conditions and ineffective collision analysis

In this section, double-contact collision model is considered for androgynous connection mechanism SMALL. Under the premise of compact and simple design, there is a great risk of interference between adjacent optical mirrors so that collision point should be determined. To simplify contact model during the docking process, three hypotheses are introduced:

(1) The shaking of flexible support structure mounted on the mirror body should be ignored;
(2) The eccentric center of mass of PMA is not taken into consideration;
(3) The thrust eccentric of the docking process is not taken into account.

In order to readily distinguish two docking modules, as shown in Figs. 4(a) and 4(b) are exactly the same simplified illustrations of SMALL. A1 and A2 represent the grooved pin and entrance hole of mechanism A, respectively. Similarly, B1 and B2 represent the grooved pin and entrance hole of mechanism B, respectively. In the following section, a common docking process will be discussed using A and B.

Fig. 4 Schematic diagram of docking process.

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When the distance between A and B reaches the effective capture range, the pins make contact with opposite holes. The determination of the range of entry capture mainly relies on the collision position and the deflection angle of grooved pins. The global coordinate system OXYZ is established through A2 as shown in Fig. 5. The origin O is located at the intersection of extension lines of the A2 tapered hole generatrix. Z axis coincides with the cone axis of A2.

Fig. 5 The coordinate system in capture stage.

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It is assumed that for this docking process, the first contact occurs between A2 and B1 and then B2 and A1 afterΔt time. (Based on this condition, if the cones and the pins of two connective mechanisms parallel to each other and make contact at the same time, Δt is regarded as 0.)

The collision of A2 and B1 is shown in Fig. 6, where $V^{0}$ represents the velocity of the contact point before impact. Similarly, $V^{1}$ represents the velocity of the contact point after impact. $ε_{0}, ε_{1}$ represent the entrance angle and the exit angle, respectively. β represents the half cone angle of A2.

Fig. 6 The trace of the pin in the chamfered hole.

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In capture stage, the velocity ratio before and after the collision is defined as the recovery factor, which can be written by

S = | \frac{V_{k}}{V_{0}} | .

In order to move the pin towards the bottom of the chamfered hole without generating a reversible or a viscous collision after the first contact, it can be seen from the Fig. 6 that the following condition needs to be met:

ε_{1} < 90 ° - 2 β .

We need to explore the relationship between the exit angle

ε_{1}

and the entrance angle

ε_{0}

to meet the inequality above. Due to the impact impulse, the velocity after the collision of the inserted pin B2 is

{\begin{matrix} V_{n}^{1} = S V_{n}^{0} \\ V_{τ}^{1} = V_{τ}^{0} + (1 + S) T V_{n}^{0} \\ T = M \sum_{i}^{2} (\frac{\sin μ}{m_{i}} + \frac{r_{i}^{2} \cos θ_{i} \sin (θ_{i} - μ)}{I_{i z}}) (i = A, B) \end{matrix},

where

V_{n}^{0}

,

V_{τ}^{0}

represent the normal and tangential velocities of the contact point before impact; Similarly,

V_{n}^{1}

, $V_{τ}^{1}$ represent the normal and tangential velocities of the contact point after impact; M is the equivalent mass of the docking mechanism; T is the equivalent stiffness;

I_{i z}

is the moment of inertia around the Z axis of the mechanism;

θ

is the angle between the vector of the two docking mechanisms centroid to collision point and the normal of the cone; μ is the coefficient of friction angle of conical surface.

From the Eq. (3), the $ε_{1}$ can be represented by:

\tan ε_{1} = \frac{V_{n}^{1}}{V_{τ}^{1}} = \frac{S \tan ε_{0}}{1 + (1 + S) T \tan ε_{0}} .

From the geometry relations shown as Fig. 6, it is easy to formulate the insertion motion state as:

\tan ε_{1} = \frac{S}{\frac{1}{\tan ε_{0}} + (1 + S) T} < \tan (90 ° - 2 β) .

Surly the Eq. (5) can be written by:

S < \frac{\frac{\tan (90 ° - 2 β)}{\tan ε_{0}} + \tan (90 ° - 2 β) T}{1 - \tan (90 ° - 2 β) T} .

As long as a reasonable control law of the double-contact collision velocity ratio is given into the docking process, one of the two contact points will not generate failure collision. In the next section, the collision of the other collision point will be discussed.

At the collision point M, tangent to the normal plane of the A2 axis, the local coordinate system O’X’Y’Z’ as shown in Fig. 7 is obtained. After the collision between A2 and B1, the location of the other collision between A1 and B2 needs to be determined. With B1 as the center, the B2 position is theoretically distributed on the circle of C₀ whose radius is equal to the distance of the axis between the entrance hole and the inserted pin in the mechanism B.

Fig. 7 Contact points distribution in the double-contact model.

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Given that the local coordinate system O’X’Y’Z’ is located at the collision point, the coordinates of B1 are assumed to be (x_b1’, y_b1’, z_b1’) and the coordinates of B2 are assumed to be (x_b2’, y_b2’, z_b2’). The distance between B1 and contact point M is assumed to be r₁. For capture process, when $\bar{M B_{1}} \leq r_{1}$ , it is considered that contact has occurred. Intrusion is:

δ {=r}_{1} - \bar{M B_{1}} .

According to the geometric relationship of the Fig. 7, the coordinates of the collision point M are:

(\frac{| x_{b 1}^{'} z_{b 1}^{'} \tan β |}{\sqrt{{(x_{b 1}^{'})}^{2} + {(y_{b 1}^{'})}^{2}}}, \frac{| y_{b 1}^{'} z_{b 1}^{'} \tan β |}{\sqrt{{(x_{b 1}^{'})}^{2} + {(y_{b 1}^{'})}^{2}}}) .

r₁ can be expressed as:

r_{1} = | z'_{b 1}^{} | \tan β - \sqrt{(x'_{b 1}^{}^{2} + y'_{b 1}^{}^{2})} .

With A2 as the circle center as well as the distance from A2 to the collision point M as the radius, the circle equation in coordinate system O’X’Y’Z’ is expressed by:

{\begin{matrix} {(y_{2}^{'})}^{2} + {(x_{2}^{'})}^{2} = {(z_{2}^{'} \tan β)}^{2} \\ \frac{r_{h}}{\tan β} \leq z_{b 1}^{'} \leq L_{0} \cos β \\ r_{h} \leq | y_{b 2}^{'} | \leq L_{0} \sin β \end{matrix} .

The straight-line equation of pin-hole

\bar{B 1 B 2}

of connective mechanism B can be obtained by:

y_{B}^{'} = \frac{y_{b 1}^{'} - y_{b 2}^{'}}{x_{b 1}^{'} - x_{b 2}^{'}} x_{B}^{'} + \frac{x_{b 2}^{'} y_{b 1}^{'} - x_{b 1}^{'} y_{b 2}^{'}}{x_{b 2}^{'} - x_{b 1}^{'}} .

If:

{\begin{cases} k = \frac{y_{b 1}^{'} - y_{b 2}^{'}}{x_{b 1}^{'} - x_{b 2}^{'}} \\ b = \frac{x_{b 2}^{'} y_{b 1}^{'} - x_{b 1}^{'} y_{b 2}^{'}}{x_{b 2}^{'} - x_{b 1}^{'}} \end{cases},

the Eq. (11) can also be depicted as:

y_{B}^{'} {=kx}_{B}^{'} + b .

Taking the need to capture success into account in the actual docking situation, we can find that the slope k of line B1B2 needs to be guaranteed in the range of $\bar{B 1 B 2'}$ and $\bar{B 1 B 2 "}$ , so when:

{\begin{cases} k \in [0, \frac{2 L_{s} | y_{b 1}^{'} | - 2 | x_{b 1}^{'} y_{b 1}^{'} |}{{(L_{s} - | x_{b 1}^{'} |)}^{2} - {(z_{b 1}^{'})}^{2} + {(x_{b 1}^{'})}^{2}}], y_{b 1}^{'} \geq 0 \\ k \in [- \frac{2 L_{s} | y_{b 1}^{'} | - 2 | x_{b 1}^{'} y_{b 1}^{'} |}{{(L_{s} - | x_{b 1}^{'} |)}^{2} - {(z_{b 1}^{'})}^{2} + {(x_{b 1}^{'})}^{2}}, 0), y_{b 1}^{'} < 0 \end{cases},

the capture can be implemented for this type of double-contact androgynous connective mechanisms. At the beginning of the capture stage, we first confirm the initial incident velocity to avoid ineffective collision. After knowing the location of the first-drop collision point, the range of the second drop can be determined so that the subsequent capture process continues.

3.2 Analysis of viscous collision

Viscous collision refers to the state in which the relative speed of the docking mechanisms is zero after the initial collision so that the pins do not move towards the bottom of tapered holes. To avoid this failure condition, when B2 and A1 make the first contact after reaching the capture stage, the B2 will move forward to the bottom of A1 as well as the rolling motion of mechanism B will occur, leading to collision and deeper intercourse between A1 and B2.

B1 collides with elastic inner-wall of A2 with non-zero incident angle ε₀. As shown in Fig. 8, the contact surface produces tiny intrusive deformation features. The pin mass is represented by m. The center of mass of the pin collides with the elastic wall A2 in the position i at the velocity v⁰ and the incident angle ε0. The location where the pin B1 produce the maximum intrusion value of δ is position ii. The pin B2 leaves the elastic wall at the iii position through the exit velocity v_k and exit angle ε₁. The entire collision sliding distance is L_p.

Fig. 8 Intrusive deformation on the contact surface.

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A local coordinate system o’x’z’ is established with the contact initial position i as the origin. Dynamic friction factor μ is defined as the ratio of tangential vector P_t to normal vector P_n as:

μ = \frac{P_{t}}{P_{n}} = \frac{\int_{0}^{Δ t} T d t}{\int_{0}^{Δ t} N d t} = \frac{\int_{0}^{Δ t} m \frac{d^{2} z'}{d t^{2}} d t}{\int_{0}^{Δ t} m \frac{d^{2} x'}{d t^{2}} d t},

where T stands for tangential force and N represents normal force. The collision time is indicated by Δt.

According to the boundary conditions of positions i and iii, we got:

{\begin{cases} (_{\frac{d x'}{d t}) 0} = v_{o} \sin ε_{0} \\ \frac{d x'}{d t} = - v_{k} \sin ε_{1} \end{cases}

{\begin{cases} (_{\frac{d z'}{d t}) 0} = v_{o} \cos ε_{0} \\ \frac{d z'}{d t} = v_{k} \cos ε_{1} \end{cases} .

Through the establishment of the dynamic friction factor μ, further analysis of the relationship between the velocity before and after the collision is shown as below. The entire stage of process is considered as intrusion and recovery. To implement the efficient collision, there should be

{\begin{cases} P_{N} =m (_{\frac{d x'}{d t}) t} - 0 \\ P_{T} =m (_{\frac{d z'}{d t}) t} - m (_{\frac{d z'}{d t}) c} \end{cases},

in recovery stage. P_N and P_T refer to the normal and tangential vectors of the recovery stage, respectively. t is the time of the entire collision process and c indicates the time of the end of the intrusion stage.

In intrusion stage, there should be:

{\begin{cases} P_{N} = 0 - m (_{\frac{d x'}{d t}) 0} \\ P_{T} =m (_{\frac{d z'}{d t}) c} - m (_{\frac{d z'}{d t}) 0} \end{cases},

where

{(\frac{d z'}{d t})}_{c} = {(\frac{d z'}{d t})}_{0} - μ {(\frac{d x'}{d t})}_{0}

{\begin{cases} P_{T} = μ P_{N} \\ (_{\frac{d x'}{d t}) t} = - e (_{\frac{d x'}{d t}) 0} \end{cases} .

We got

{(\frac{d z'}{d t})}_{t} = {(\frac{d z'}{d t})}_{0} - μ (1 +e) {(\frac{d x'}{d t})}_{0},

where e refers to the Newton’s coefficient of restitution. To avoid inverted sliding or viscous sliding during the entire collision process, tangential conditions are need to meet

{(\frac{d z'}{d t})}_{t} > 0

. So:

{(\frac{d z'}{d t})}_{0} > μ (1 +e) {(\frac{d x'}{d t})}_{0} .

The Eq. (23) can also be rearranged as:

μ < \frac{1}{\tan ε_{0} (1 + e)} .

In this way, the relationship between the initial angle of incident velocity and the dynamic friction factor μ during the collision process is obtained. Satisfying the relationship above, the pins will continue to move toward the taper hole to avoid failure collision.

4. Locking design and sequence of SMALL

In this section, we discuss the locking design and sequence of the proposed mechanism. The connection performance of SMALL is of significant importance after two pins enter corresponding tapered holes. Different from previous connective mechanisms, SMALL for space mirror assembly needs to meet requirements including accurate location and reliable locking. Figure 9 is illustrated to show the operation of locking stage, where one of the twelve locking teeth is chosen to describe the details.

Fig. 9 Locking sequence of SMALL: (a) the initial position of locking. (b)Expansion of the locking teeth. (c)Contact between conical surface and the teeth. (d) The termination position of locking.

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When the insertion heads of a pair of SMALLs enter the bottom of the entrance holes of each other, five DOFs of the combination are restricted except one along insertion direction, including four DOFs perpendicular to the insertion direction and one rotational DOF parallel to insertion direction. The locking stage starts when the insertion head makes contact with the upper end of the locking teeth, which is shown in Fig. 9(a). The insertion head has the same taper as the upper end of locking teeth. After the locking teeth contact with the pin, these teeth will be opened outwards so that the spring moves down and accumulates energy, as shown in Fig. 9(b). When the teeth reach cylinder surface of the pin, the expansion of locking teeth and compression of the spring will be maintained, as illustrated in Fig. 9(c). When the upper locking teeth move to the locking groove of the inserted pin, a locking trigger occurs. The locking teeth are quickly pressed into the locking groove as soon as the compressed spring rebounds and reinforces the outside of the locking teeth to prevent the docking mechanisms from breaking open, as Fig. 9(d) shows.

Before the locking trigger happens, locking process has gone through two stages: one stage is the moment when the cone surface of the pin head makes contact with the locking teeth. At this moment, the diameter of locking teeth is continuously enlarged and the spring persistently moves down; the other stage is the cylinder surface of the pin head makes contact with the locking teeth. In this stage, the diameter of the locking teeth is constant and the length of the hoop spring remains stable.

Therefore, the resistance of the propelling force reaches maximum at the end of the first stage, which is the intersection between cone surface and cylindrical surface. At this point, the elastic restoring force of the locking teeth reaches its maximum and there are also contact friction and resilience of the hoop spring.

5. Simulation analysis of SMALL

In this section, to validate the proposed docking design methodology and the influence of gap error to optical performance, simulation studies of the SMALL within modular PMA are organized as follows.

5.1 Dynamic performance analysis

In order to test and verify the feasibility of the SMALL, there should be a stack of parameters with no gravity environment such as axial docking velocity, lateral deviation and roll angular velocity. One PMA keeps stationary in the center to which another PMA is free to approach via the parameterized docking maneuver. According to SPHERES docking experiment parameters [24] and docking data from Automated Rendezvous and Docking of Spacecraft [25], the typical initial docking conditions of SMALL are listed in Table 2.

Table 2. Initial docking conditions of SMALL

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The simulations are designed including typical maximum lateral bias errors and roll angular velocity during the docking process. The material of SMALL and the base is aluminum alloy 6061. The coefficient of friction between the grooved pin and the entrance hole is 0.3. A docking coordinate system is established at the center of mass of the settled PMA. The Y axis indicates the axial direction of the mechanism while X axis is paralleled to the plane formed by the axes of the pin and hole. The initial axial docking velocity is 5mm/s.

It can be seen from Fig. 10 and Fig. 11 that the entire capture time is 0.58s. Figure 10 shows the relationship between displacements (mm) and capture time (s), where the offset distance is 8 mm. The first contact occurs at 0.17 s. As shown in Fig. 10(a), the x-direction curve which is parallel to the pin-hole plane has a large displacement fluctuation because of the rebound after the collision. In contrast, the displacement in the z direction illustrated in Fig. 10(c) has little effect on the capture process. The y direction indicates the effective capture direction, as shown in Fig. 10(b). Figure 11 shows that there are triple contacts during capture process, which have diminishing effects. The first contact timing has a clear chronological order of two contact points as we assumed in Section 2. Invasion denial happens when the limiters of the grooved pins make contact with the chamfered holes to prevent the further interaction. The force of invasion denial is far greater than that of collisions, which also meets design expectations. So the typical capture process can be described as one pin first collides with the corresponding hole, causing the other pin to contact with the opposite hole, thus after shock contacts and slip entrance, the docking stage is finally completed under the protection of limiters of the grooved pins.

Fig. 10 The displacement trace of the inserted pin head: (a) x-direction. (b) y-direction. (c) z-direction.

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Fig. 11 Contact force of two contact points.

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5.2 Error distribution and optical performance analysis

In the actual assembly process of the on-orbit optical system, due to the existence of manufacturing and assembly errors, the final error may cause the optical performance of the telescope to decline. The main factors affecting the optical performance include optical design residuals, optical processing errors, optical assembly errors, and environmental influences. In optomechanical integration process, there are some factors causing performance degradation of the optical system, such as the tip and tilt error of each PMA, the gap error of connected PMAs, and the surface shape error caused by the deformation of the backplane supporting system of PMA. In order to analyze the influence of the gap error between two connected PMAs, an optical system is designed. The design parameters are shown in Table 3.

Table 3. Optical system parameters

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The influence of the wavefront aberration on the imaging quality can be evaluated by the Strehl Ratio (S) of the optical system. The relationship between S and the total wavefront aberration is:

{S=e}^{- (2 π W / λ)}^{^{2}},

where W is the root mean square value of the wavefront aberration and λ is the reference wavelength.

Optical requirements should be satisfied when S = 0.8 according to the imaging quality requirements. Then W = 0.1λ is obtained at this time. Therefore, the corresponding Root Mean Square (RMS) wavefront aberration should not exceed 0.1λ (λ = 632.8 nm). In order to analyze whether the gap error between two connected PMAs can meet the requirements of the design specification, the aberration of the optical system needs to be reasonably distributed. The RMS wavefront aberration is used as a basis for error distribution. The overall wave aberration can be divided into optical imaging performance error and defocus error, in which the defocus error is assigned as 0.016λ, and the optical imaging performance error is assigned as 0.0987λ, as shown in Fig. 12.

Fig. 12 Error distribution of RMS wavefront aberration of PM.

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For a modular assembled optical system, the PM component consists of a plurality of small-sized PMAs. For the adjustment of the entire PM assembly, adjustment error can be divided into the overall PM alignment and the PMA opto-mechanical integration. The overall PM alignment is divided into centrifugal error, tilt error and position error, as shown in Fig. 12. The corresponding error distribution results are ± 0.11 mm, 50 nr and ± 37.5 mm, respectively, and the wave aberrations are 0.02λ, 0.017λ and 0.03λ, respectively. The PMA opto-mechanical integration includes gap error, tilt error, rotation error, position error, and surface error. In this study, after the two modules are docked, SMALL performs the adjustment process mainly to correct the gap error. The purpose is to reduce rigid body errors in the individual PM segment so that the overall segment level gap error is less than about 0.03λ, not counting tip, tilt, or piston errors.

In the evaluation of optical system imaging quality, the error perpendicular to the optical axis mainly refers to the mirror gap error. According to the error distribution calculation results in the Fig. 13, the gap error should be kept within 2 μm. The relationship between the Strehl Ratio and gap error of PMAs is shown as Fig. 14.

Fig. 13 Error distribution of PMA wavefront aberration.

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Fig. 14 (a) The relationship between Strehl Ratio and the X position error; (b) The relationship between Strehl Ratio and the Y position error.

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As can be seen from Fig. 14, the gap errors in X and Y direction are negatively correlated with Strehl ratio. If there is no gap error between two segmented mirrors, the Strehl ratio is 1. When the gap error reaches a maximum value of 2 μm, the Strehl ratio reaches a minimum of 0.982. At this time, the Strehl ratio is still within a reasonable range for good optical quality. Therefore, the gap error with the range of 2 μm satisfies the adjustment requirement of the optical system.

6. Conclusion and future work

In this paper, a connection mechanism called SMALL is designed and implemented for autonomous self-assembly of space-segmented mirrors, which is compact, androgynous and power efficient for massive assembly tasks. The proposed mechanism adopts passive locking mode and overcomes alignment errors in coarse phase in the optical chain.

The dynamic and optical performance of SMALL are analyzed. The dynamic performance sets up a double-contact model in capture stage to discuss the relationship of initial velocity and contact force, which indicates good consistency between simulation and theory. The optical performance explores the gap error of two PMAs. The error distribution results show that the gap error within 2 μm meets the optical requirements.

Our future work will focus on the data interaction of the two connected modules, since the connection mechanism is the only connection channel between the two modules. The objective is to facilitate the global alignment of the modular assembly optical system.

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Parameters	Value
Dimensions (mm)	233 × 148 × 87
Mass (g)	1163
Grooved Protruding Pin Length (mm)	79
Entrance Hole Angle × Depth × Internal Diameter (° × mm × mm)	60 × 17 × 20
Positioning Diameter × Depth (mm)	20 × 30
Actuator Length (mm)	50
Actuator Linear Resolution	0.1%ForceTime
Linear Motor Voltage (V)	150

Parameter	Value
Focal length (mm)	80000
Pixel size (μm × μm)	25 × 25
Field of view (°)	0.28
Wave length (μm)	0.3 – 0.5

Parameters	Value
Dimensions (mm)	233 × 148 × 87
Mass (g)	1163
Grooved Protruding Pin Length (mm)	79
Entrance Hole Angle × Depth × Internal Diameter (° × mm × mm)	60 × 17 × 20
Positioning Diameter × Depth (mm)	20 × 30
Actuator Length (mm)	50
Actuator Linear Resolution	0.1%ForceTime
Linear Motor Voltage (V)	150

Parameter	Value
Focal length (mm)	80000
Pixel size (μm × μm)	25 × 25
Field of view (°)	0.28
Wave length (μm)	0.3 – 0.5

Design, analysis of self-configurable modular adjustable latch lock for segmented space mirrors

Abstract

1. Introduction

2. Design requirements and operation principle

3. Contact analysis in capture stage

3.1 Initial capture conditions and ineffective collision analysis

3.2 Analysis of viscous collision

4. Locking design and sequence of SMALL

5. Simulation analysis of SMALL

5.1 Dynamic performance analysis

5.2 Error distribution and optical performance analysis

6. Conclusion and future work

References and links

Cited By

Figures (14)

Tables (3)

Equations (25)

Optics Express