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Minimized Converging Single-Point (MConS) Kinematics: a Novel Approach to Fastening Detachable Spacecraft Structures

Jared Leidich1 Paragon Space Development Corporation, Tucson, AZ, 85714, USA

The process of connecting or detaching separate bodies in space can be aided very readily by the use of kinematics. A kinematic mounting system, as the definition will be used in the context of this topic, is a structural bond created solely by the geometry of a surrounding structure and a structure being bound. The use of kinematics can have very significant advantages over traditional fasteners like bolts and traditional clamps if certain features are utilized. The use of converging kinematics provides the highly beneficial feature of tending a system towards a certain stable equilibrium from a range of starting locations that meet the requirements of a set of initial conditions. Many space systems have a very apparent need for various levels of alignment in a fastening system where complex alignment mechanisms are difficult to actuate. In a convergent system such as the one in the theory being proposed, a force need only be applied in one direction and the binding structure will align the structure being bound using the available geometric surfaces leaving the child structure in a fastened, aligned position after the application of a force in a single direction. Convergent systems work in parallel with single-point kinematics where necessary. The term single point kinematics is referring to the utilization of only point contacts. Traditional optical kinematic systems utilize theoretical line-contacts. The advantages of using point contacts exclusively are in the conductive properties of single-point contacts. Single points of contact offer excellent thermal isolation which is a very desirable feature in many spacecraft applications. Depending on the load being applied to the structure, the contact patch between a convex mount and a theoretically flat female surface can be extremely small in which case the conductive resistance as a function of contact area will be approaching zero. Using single-point contacts, if the number of contact points is minimized, the thermal performance of the system can be maximized. The minimization of necessary contact points to constrain a system in three dimensions has been found through a geometric investigation to be mathematically related to the number of translation and rotation modes being acted against. This geometric analysis provides a theory as to the minimum number of points needed to constrain any system with forces acting in know modes of translation or rotation. The three main points of potential benefit for the system being proposed include the use of converging surfaces for aid in alignment and to allow for the potential use of single-point contacts to isolate the thermal conductance paths between two structures. Combined with these features a novel geometric analysis was performed to find the least number of contact points that were necessary to fully constrain a rigid body. In a system needing support or restriction in all three translation modes (X, Y, and Z) and all rotation modes (roll, pitch, and yaw) a kinematic bounding using single point contacts could be optimized to be a highly conductively isolated structural contact system.

Nomenclature Nmounts = Number of contact points Nmodes = Number of available modes of movement

1 Aerospace Engineer, Engineering, 3481 E Michigan St. Tucson, AZ, Member.

AIAA SPACE 2010 Conference & Exposition 30 August - 2 September 2010, Anaheim, California

AIAA 2010-8762

Copyright © 2010 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

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I. Introduction n the unique environment of space vacuum several systematic factors become very pertinent that typically would not be in a terrestrial one. Perhaps the most important factor when designing machinery for space is that it is

mostly inaccessible by humans after launch. This makes simple operations like taking things apart and putting them back together (for whatever reason) with any sort of necessary alignment a very difficult task. In that context a system that could start from a wide range of initial conditions and systematically align itself during the fastening process could be highly beneficial for any structure that needs to connect with another structure in space. Another important consideration for space design is the impact of thermal vacuum on controlling the heat moving into, out of and through a spacecraft. In a terrestrial environment where convective heat transfer tends to dominate interactions between a body and its ambient surroundings less emphasis needs to be put on minimizing conductive and optical heat transfer than on convective transfer. For that reason, somewhat contrary to terrestrial heat transfer problems, isolating the thermal contact area between high temperature areas and temperature sensitive regions of a spacecraft is crucial in certain applications, and in general having the ability to thermally isolate parts of a spacecraft could make the thermal design of a spacecraft more robust and certain. Given these considerations MConS Kinematics aim to simultaneously improve the ability of a spacecraft to attach and align itself to a different structure and isolate the two systems from one another thermally. A specific design has been examined and analyzed in previous works.1

II. Background MConS kinematics were initially designed for the Small Payload Quick Return (SPQR) program. The SPQR vehicle is being developed by NASA Ames as a thermally controlled on-demand downmass solution for the International Space Station (ISS). The system is planned to be actuated by astronauts on board the ISS so needed to be very easy to assemble, so was designed to be self aligning and constrained by the application of a single force. The system then needed to survive an atmospheric reentry at close proximity to the hypersonic reentry gasses which constituted the requirement of excellent thermal isolation.

A. Traditional Kinematics Kinematics are traditionally used in optics to provide a precision alignment mechanism to mounting systems. The most common configuration is the cup-trench-plane system. As can be seen in Figure 1 these traditional systems utilize 3 point-contacts and on line contact. This type of mount would offer good thermal isolation, however the structural mechanism applying the force on the system typically runs between the two structures providing a large thermal highway for heat transfer negating the isolation affects of the tiny contact areas.

B. MConS Kinematics without a Rotational Constraint The first version of the MConS kinematic system was designed as simply as possible within the requirements provided by the customer (NASA ARC). This system was designed originally in two dimensions for the sake of simplicity and to geometrically define the system limits and parameters. As can be seen in Figure in the two dimensional representation there are two “V” structures essentially binding a component between them, as long as the angle on the “V” structure is steep enough the system will tend towards stability and fully constrain in two dimensions. As can be seen in Figure 2 when the “V” structures are revolved into three dimensional cones the system is then resting on six points of contact and is constrained in all translation modes and two of three rotation modes (the system as a rigid body is allowed to rotate about the central axis). This design adequately filled the need for the specific application but was considered inadequate as a universal design due to its lack of full constraint and a known final position.

I

Figure 1: Traditional Kinematic Mounts [1]

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III. The Three Pertinent Features of MConS Kinematics The three features that make MConS Kinematics unique and potentially beneficial to the space industry are that they are convergent, utilize single point contacts, and have a mathematically minimized number of single contact points.

A. Convergent The first important feature of this system is a tendency to converge within a set of initial conditions. This tendency can take two structures with very poor initial alignment (essentially not aligned) and bind them while taking that alignment to a very high precision (depending on the precision of the two structures being fastened). The convergence relies on a double conic system that forces the structure being bound to align with the binding structure.1

B. Single Point Contact Kinematic systems are traditionally used in optics to provide precision alignment. While kinematic systems have a very wide variety of configurations, including those utilizing point contacts2, the structures often rely on line contacts and bolts directly from the kinematic body to the parent structure which relies on bolt plane contacts. This is practical for systems used exclusively for alignment, however when considering thermal control, a bolt contact provides a large avenue for thermal transfer. Additionally, while convergence is a prerequisite for precision alignment, the convergence area (or initial condition range for convergence) typically is not the driving factor in starting position because the bolts need to line up in order to start the actuation of the system; this makes the ability of a system to converge from a large range of initial conditions very limited.

Figure 2. Two dimensional representation The lower angled structures represent the aft fixedstructure, and the upper angled surfaces representthe axial constrained fore mount fixture. [1]

Figure 2. Three dimensional representation The lower cone is fixed and the upper cone is constrained to share an axis with the lower cone. [1]

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In an MConS kinematic system the only contact points between the binding structure and the bound structure are single points; fasteners would be needed to hold the mounts in place, but those fasteners would all be internal to the separate structures and would not cross between them.

C. Minimized Point Contacts A geometric analysis was performed in an attempt to find the smallest number of contact points that could be used to constrain a rigid body in three dimensions.

1) In one dimension the geometry model is very simple and allows a conclusion to be drawn easily. As can be seen in Figure 3 there is only one mode of translation in one dimension in the X direction, and no rotation modes. In this model the dotted line represents a one-dimensional universe and the line represents a rigid body. By inserting a constraint (a point) the body is left unconstrained. If a second constraint is inserted the body can be fully constrained. From the one dimensional analysis it is easy to conclude that it requires at least one more constraint point than translation modes to fix a rigid body.

Figure 3: Constraining a Rigid Body in One Dimension

2) In two dimensions the geometries become slightly more complex, but still allow a more simple investigation than the problem itself which resides in three dimensions. In Figure 4 the plane represents the two dimensional universe, and the tripod shape represents a two-dimensional rigid body. One point of contact cannot restrict the motion of the body in any modes. If the second point of contact is opposite the first it could constrain the body in one translation mode (X). A third point of contact can constrain all translation modes (X and Y) but not the rotational mode. Four points of contact can constrain the system in all rotation and translation modes in two dimensions.

Figure 4: Constraining a Rigid Body in Two Dimensions

First contact point

One dimensional rigid body (a line)

Second contact point

One contact point Two contact points Three contact points Four contact points

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3) From the analyses done in one and two dimensions the apparent relationship between modes of translation

and rotation is number of translation modes plus number of rotation modes plus 1. As can be seen in equation 1, this simple hypothesis would proclaim that a fully constrained system can be created in three dimensions using seven contact points. As can be seen Figure 5 seven points of contact can fully constrain a system in three dimensions as the theory would pose.

1mod esmounts NN (1)

Figure 5: Constraining a Rigid Body in Three Dimensions

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IV. Optimizing the Shape of the MConS Surfaces The shape presented while displaying the fully constrained seven point contact version of this system is not very ideal for production or practical use. Ultimately four surfaces need to converge radially and laterally to pull a child structure into alignment with a sloped parent structure using the application of a single force. As can be seen in Figure 6 to do this a lofted face moving from a division point to a four plane radially and laterally converging body could pull a structure from any point within the circular domain of the cone footprint to a locked know position when the structures are pulled together. 2

V. Scalability The original MConS kinematic system was designed for a small reentry vehicle (~20 kg) with an approximate diameter and length of 6.5 and 19 inches respectively. As can be seen in Figure 7 below the original system is round and bound within a canister. The system bound by a canister works very well because the inner structure is forced to reside within the necessary initial conditions, however the canister constraint is not a required feature for functionality. While the system was analyzed specifically for this size vehicle there is reason to believe a similar configuration could be used on very small components that need to be replaced or otherwise removed and attached or very large structures like primary payloads. As systems get larger the deformation of the mounts increases resulting in larger contact patches and more conductive heat transfer, this heat transfer should be proportional to overall vehicle size and possibly an acceptable increase given the larger structure. An identified limiting factor to overall size is material properties of the mounts.

2 The final convergence position within the conic footprint would actually be one of two known positions depending on where the structure started but would always end fully constrained. Future work may include a potential design converging the structure from any radial starting point to a single known position.

Figure 6: Fully Constrained MConS Kinematic System with a Radially Convergent Cap

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At some overall system size it could be anticipated that a point load would cause a high enough strain around the contact location that the material would yield and render the mounts ineffective from that point forward. The proper analysis has not been performed to verify at what point this would happen but from the results of a moderately sized system it appears that the mounts could grow several times in size before reaching the material limits of most typical mount materials like hardened steel or titanium.

Figure 7: Mid Size MConS Kinematic System

VI. Possible Application of MConS Kinematics The advantages of MConS kinematics in convergence and thermal isolation make the system ideal for any components that can be aided by thermal isolation and need to be detached and / or reattached during their lifetime in space. The already identified use is for human integrated reentry vehicle payload canisters. An additional identified potential application for MConS kinematics would be a largely scaled up version used for docking spacecrafts. A system that aligns a spacecraft from an arbitrary starting point and takes it to an aligned position could be highly beneficial. Additionally, when docking a spacecraft the thermal concerns can become very complex if the structures are sharing thermal environments. The Space Station for instance collects more solar radiation when a spacecraft is docked to it changing the systematic heat loads and making the design and analysis for the changing environment more complex, an MConS kinematic system would drastically reduce the amount of heat transfer between the bodies so they could potentially be treated as separate entities during heat transfer analysis. While MConS kinematics were developed for space application technologies, the system could be applied to both space applications and terrestrial systems. The main reason Kinematics are a good fit for evacuated environments is the lack of convective heat transfer. Without convective transfer conductive and radiative transfer become the two dominant modes of heat transfer giving them much more emphasis. These features however do not detract from the unit’s ability to align two components from a wide range of initial conditions and reduce conductive heat transfer which could benefit a wide variety of terrestrial mechanical components.

VII. Conclusions A universally designed MConS kinematic system could offer two major benefits to thermally focused spacecraft structures including convergent surfaces to tend the system towards stable equilibrium from a wide range of initial conditions and conductive thermal isolation. In anything from small removable components to entire spacecrafts MConS kinematics can provide an easy alignment tool and thermal protection system in space and potentially in the future on earth.

Fore kinematic interface

Aft kinematic interface

~6.5 inches

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Acknowledgments F.A. Jared Leidich thanks Paragon Space Development Corporation for their support of the development of these

ideas. F.A. Jared Leidich would also like to thank James Izlar for his contributions to the concept being developed.

References 1 Leidich, Jared, Davis, Bruce “Development of a Structural Kinematic Mounting System for Small Payloads,” International Conference on Environmental Sciences, AIAA-2010-6145, Barcelona, Spain, 2010 2 Hale, Layton C., Slocum, Alexander H. Optimal Design Techniques for Kinematic Couplings, Precision Engineering, Volume 25, Issue 2, April 2001, Pages 114-127