ai-aerospace/ams_data_full_2000-2020 huggingface dataset:
328 4. Upon landing, the landing pads will remain fixed relative to one another as they were in the  undeflected configuration; landing impact will not affect the placement of individual pads on the  ground. 

Leg Numbering System   Figure 1 and Figure 2 show the leg numbering system that is used to describe joint orientations.  

Figure 1. Top view of module with legs numbered    

Figure 2. Front view of module with legs numbered   Joints

As mentioned previously, each leg will have a joint t hat connects the leg to the module. For the analyses  presented here these joints will be flexures whose be nding axes are perpendicular to the plane formed by  that leg and the opposing leg when the landing gear is in its undeflected configuration. For example, in Figure 2 the flexure axes of legs 1 and 3 will be out of the page while the flexure axes of legs 2 and 4 will be parallel to the page. For each leg, this flexure will be called flexure f.   Additionally, the joints that connect the legs to the landing pads will be spherical joints and thus will not  have any resistance to rotation.  Next, the joint in the middle of each leg will be the flexure equivalent of a universal joint with perpendicular axes. This is accomplished by having two flexures serially connected as depicted in Figure 1. One of the bending axes will be parallel to the bendi ng axis of the joint which connects the leg to the  module while the other axis will be in the plane formed by that leg and the opposing leg. For each leg, the 1 3 2,41 2  3  4  NASA/CP-2010-216272
329 flexure with the bending axis parallel to  that leg’s bending axis of flexure f  will be called flexure d while the  serially connected flexure will be called flexure e.  

Because it has been shown that flexures can be mode led as linear torsion springs, subsequent modeling  will assume that the flexures are traditional revolute or universal joints with torsion springs to resist rotation about the bending axes. For the model of each analysis, it is assumed that the bending axes of flexures d and e  both pass through the same point. 

Figure 1. Universal flexure created by serially connecting two flexures [2] 

Analysis   Two-Dimensional Analysis

The first analysis performed was a two-dimensional analysis in which the plane that was analyzed was  that which is formed by two opposing legs in the undef lected configuration. The active flexures for the  planar analysis of legs 1 and 3 are shown in Figure 4.  It can be seen that legs 2 and 4 together form a  single middle leg that has one flexure. Additionally, to  account for the change in length of legs 2 and 4  projected onto the plane due to the out of plane motion,  the middle leg is of variable length. This variable  length is depicted in Figure 4 by a double headed arrow.  

Figure 2. Joints and links for planar analysis   The three spring stiffnesses will be determined as follows:  1. Give an initial guess of spring constants for flexures d, e, and f.   2. For a given ground slope find the angle of each joint as described below. 3. Using static balancing equations find the required lunar weight of the module such that the  combination of the weight of the vehicle and the resistance to bending in the springs will put the  module in static equilibrium. For a given set of sp ring stiffnesses there exists one unique solution  of required weight that will hold the module in stat ic equilibrium at the desired level configuration.  4. Repeat steps 2 and 3 for n steps of ground slope between 0 deg and 12 deg. 5. Calculate the average required we ight from the n steps in step 4.  6. Use forward divided differences with steps 4 and 5 to estimate the gradient of average required  weight with respect to the stiffness of each spring.  1 3  2,4f f  d d  e glunar e d  NASA/CP-2010-216272
330 7. Use steepest descent to find the set of stiffnesses ( d, e, f) that minimizes the difference between  the calculated average required weight and the known lunar weight of the module using the  estimate of the gradient from step 6 for each iteration. 

This planar mechanism has seven bodies (including the ground) and eight revolute joints resulting in two degrees of freedom. Addition of the va riable length of the middle leg gives a total of three degrees of  freedom.  Because the mechanism has three degrees of freedom, three choices regarding its configuration must be  made. The first choice, which should be the most obvious, is that the module be level with respect to the local gravity field. The second choice is the length on the adjustable leg which will account for any ground  slope going into the page. Lastly, the angle of flexure d on the uphill leg is assu med to be constant at an  angle of 180 deg. This assumption remains valid for any configuration that would otherwise try to extend  the angle beyond 180 deg if the leg is designed with a mechanical stop preventing a greater angle. An example of a configuration after these three choices is shown in Figure 5. 

Figure 5. Configuration of leveled module   Three-Dimensional Analysis

The second analysis performed was a three-dimensional analysis. This analysis looks at the mechanism as a whole instead of just a projected plane while also providing a slightly different approach to finding the  optimized spring stiffnesses.   This approach is as follows:  1. Give an initial guess of spring constants. 2. For a given ground slope and twist angle find the mechanism configuration as described below.

3. Using static balancing equations find the required lunar weight of the module such that the  combination of the weight of the vehicle and the resistance to bending in the springs will put the  module in static equilibrium. For a given set of sp ring stiffnesses there exists one unique solution  of required weight that will hold the module in stat ic equilibrium at the desired level configuration.  4. Use forward divided differences with step 3 to calculate the gradient of required weight with  respect to the stiffness of each spring. While there exists a unique solution of required weight for a set of spring constants, for the inverse proble m when given the required weight there exists a  plane of solutions for the set of spring stiffnesses.  The calculated gradient is the normal vector to  all of the planes of solutions for any given required weight.  5. Calculate the point that is closest to the init ial guess of spring constants and on the plane of  solutions when the required weight is eq uated to the given weight of the module.  6. Using the point found in step 5 and the norma l vector, calculate the equation of the plane.  7. Repeat steps 2 through 6 for m steps of twist angle between 0 and 45 deg. Because of symmetry  any twist angle can be modeled by a twist angle between 0 deg and 45 deg.  8. Repeat step 7 for n steps of ground slope between 0 deg and 12 deg.  glunar  NASA/CP-2010-216272
331 9. Using linear least squares, find the point that minimizes the L2-norm of the vector of the distance  between this point and each plane found in step 8. This point is defined to be the set of optimum  spring stiffnesses.    This spatial mechanism has ten bodies (including the gr ound), four spherical joints, four universal joints,  and four revolute joints. This gives six degrees of freedom, which means that the module itself can be positioned and oriented in any manner within its workspace.   Similar to the planar analysis, it is first necessary to find the angles of each joint to then find the optimum spring stiffnesses. Also similar to the planar analysis, the orientation is assumed to be level. This reduces  the degrees of freedom by two because the module must be level about two orthogonal horizontal axes.  The third choice of configuration is that the modu le is at some assumed height which is below its  undeflected height on a level surface. Essentially this is saying that on a level surface, the weight of the module would cause some sort of deflection in the join ts and would sink by some amount. This analysis  assumes that the height of the module will be at 90% of its undeflected height.    After these two constraints on orie ntation and one constrai nt on position, three de grees of freedom still  remain. It is assumed that the preferred leveled equilibrium configuration of the module will be one which minimizes the deflections in the flexures, where here  minimization is defined as minimization of the L 2norm of the vector of the twelve flexure deflections. Using the Matlab fmincon function, these remaining  degrees of freedom, two of which are position in the hor izontal plane and the third is the rotation in the  horizontal plane, can be found which minimize the deflections.   Results and Conclusions   For both the two-dimensional and 3-dimensional analysis, the flexure has the dimensions as depicted in Figure 6. The stiffness for flexure can be approximated in terms of its geometric dimensions as follows: 

5/2 1/22 9EbtkRπ≈  (1)   Two-Dimensional Analysis

The optimum spring stiffnesses as determined by the first analysis were found to be:      3 4 43.841 10 5.562 10 5.840 10d e fk Nmkradk⎡⎤⎡⎤ × ⋅ ⎢⎥⎢⎥=×⎢⎥⎢⎥ ⎢⎥⎢⎥ ×⎣⎦⎣⎦ (2) 

From this and the spring stiffness approximation of equation (1), the di mensions of the flexures as shown  in Figure 6 are on the order of:   0.1 0.01 0.5b tm R⎡⎤⎡ ⎤ ⎢⎥⎢ ⎥=⎢⎥⎢ ⎥ ⎢⎥⎢ ⎥⎣⎦⎣ ⎦ (3) 

Using these spring stiffnesses and the given weight of  the module a static analysis was performed for a  range of ground slopes between 0 deg and 12 deg. The maximum angle of the module in this range was 2.5 deg at a ground slope of 12 deg.  NASA/CP-2010-216272
332  

Figure 3. Flexure dimensions [2] 

Three-Dimensional Analysis   The optimum spring stiffnesses as determined by  the second analysis were found to be:       51.077 1.811 10 2.162d e fk Nmkradk⎡⎤⎡⎤⋅ ⎢⎥⎢⎥=×⎢⎥⎢⎥ ⎢⎥⎢⎥⎣⎦⎣⎦ (4) 

From this and the spring stiffness approximation of e quation (1), the dimensions of the flexures as shown  in Figure 6. Flexure dimensions are on the order of: 

 0.2 0.01 0.05b tm R⎡⎤⎡ ⎤ ⎢⎥⎢ ⎥=⎢⎥⎢ ⎥ ⎢⎥⎢ ⎥⎣⎦⎣ ⎦ (5) 

The static analysis that was performed for the ca lculated spring stiffnesses for the two-dimensional  analysis has not yet been performed for the three-dimens ional analysis. This will be completed in future  work.  Comparing the results of the two analyses it is se en that the optimum stiffness as found by the twodimensional analysis is only about one-fourth as that obtained from the three-dimensional analysis. This discrepancy is likely due to the different assumptions  of the two analyses, specif ically the length of the  adjustable leg and the fixed angle of the uphill leg in the two-dimensional analysis. Additionally, because  of the assumption that th e bending axes of flexures d and e pass through the same point, it follows that  the flexure radius R must be small because the flexures are actu ally serially connected. Because of this,  the three-dimensional analysis might prove more a ccurate because of this much smaller dimension. 

   NASA/CP-2010-216272
333 Future Work 

In addition to the three-dimensional static analysis for the calculated spring stiffnesses there are a few other .tasks that can improve the r obustness of this method. These incl ude calculating and minimizing the  stresses in the flexures and taking into account t he change in module weight once the payload has been  unloaded. Additionally, minimizing the effect of single-leg disturbances, such as one leg landing on a boulder or in a small crater or being displaced by l anding impact, would increase the robustness. Also, for  more insight into the actual bending mechanics, a fini te-element analysis might prove more accurate than  the linear spring approximation. Lastly, looking at different flexure shapes, as described in [3], might provide a better flexure system.   Acknowledgments 

The research of this paper was funded  by the NASA Graduate Student Researchers Program and the  University of Florida Alumni Fellowship Program. 

References 

 1. Howell, L. L. Compliant Mechanisms . New York: John Wiley & Sons, ©2001.  2. Paros, J. M. and L. Weisbord. “How to Design Flexure Hinges.” Machine Design  (November 1965), pp.  151-157.  3. Lobontiu, N. Compliant Mechanisms: Design of Flexure Hinges . Boca Raton: CRC Press, ©2003.         NASA/CP-2010-216272
335 Design and Manufacture of a Highly Relia ble, Miniaturized and Low Mass   Shutter Mechanism 

M. Manhart* , T. Zeh*, G. Preißler*, A. Hurni*, G. Peter+, I. Walter+, J. Helbert+,   K. Multhaup++ and H. Hiesinger++ 

Abstract    This paper describes the development, manufacturing and testing of a lightweight shutter mechanism  made of titanium for the MERTIS Instrument. MERT IS is a thermal infrared imaging spectrometer  onboard ESA's future BepiColombo mission to Mercury. The mechanism is built as a parallelogram arrangement of flexible hinges, actuated by a voice coil.  In a first test run, it was shown that the selected  EDM processing led to the generation of titanium oxides and an oxygen-enriched surface layer on the substrate (so called α-case layer). In the revised version of the shutter, it was possible to manufacture the  complex geometry by micro-milling and an adjacent pickling procedure. The adequacy of this approach was verified by lifetime and vibration testing.   Introduction and Requirements   The MERTIS instrument is a thermal infrared imaging spectrometer onboard ESA's future BepiColombo mission to Mercury. For the spectrometric data acquisition, a calibration signal that contains information about the instrument background radiation is required. This is performed by periodical acquisitions while  the targets scene (i.e., planet radiatio n) is blocked. Therefore, a mechanical shutter is required to block  the optical path from the planet view of the instrument.  The main requirements for the shutter mechanism are specified in Table 1. 

Table 1: Shutter main requirements 

 Requirement  Mass 25 g  Max. dimensions 20 x 40 x 5 mm3  Max. Frequency 10 Hz  Duty cycle 1:10  Lifetime test 100 x 106 cycles  Fail safe position Shutter-blade in open position  Aperture 1.5 mm x 8 mm 

                                                            * Kayser-Threde GmbH, Munich, Germany  + Deutsches Zentrum für Luft- und R aumfahrt (DLR), Berlin, Germany  ++ Institut für Planetologie, Westfaelische Wilhelms-Universitaet, Muenster, Germany 

Proceedings of the 40th Aerospace Mechanisms Symposium, NASA Kennedy Space Center, May 12-14, 2010   NASA/CP-2010-216272
336 Shutter Design  

In an extensive study, all major shutter driving princi ples have been investigated for their use in MERTIS:   rotary DC motors, linear piezo actuators/motors, pi ezo bender actuators, and linear voice coil actuators  (VCA).  An important criterion was that the majority of pos sible failures shall lead to a defined fail safe position  (i.e., shutter-blade open). Therefore, the voice coil ac tuator with a moving magnet and a stationary double  coil (HELMHOLTZ alignment) was select ed. It is simple to design a VCA mechanism where the inactive  or standby shutter-blade position is open.   Figure  1 shows the assembled shutter. Flexible hinges that enable frictionless, linear guiding were  selected to achieve the demanding lifetime requirements. The shutter consists of a parallelogram assembly with two flexible hinges that enables a nearly linear 1.5-mm movement of the rocker with its shutter-blade. Furthermore, the VCA with its movi ng magnet, the stationary double coil and a magnetic  sensor (GMR) for a position feedback signal  for the control electronics are shown.   A number of dramatic failures of flexible hinges sy stems during vibration test have been reported. For  random vibration, the high Q-factors at resonance together with high mid-frequency PSD levels can lead to high loads on the flexible hinges [1]. Furthermore, a sufficient stability against transverse loads has to be guaranteed. Two measures have been taken in orde r to prevent damage during vibration tests or  during satellite launch:    a snubber that acts as a mechanical limiter against unwanted high displacements of the rocker,    reduction of the moving mass to the smallest po ssible amount in order to limit the kinetic energy  of the rocker.  

It was possible to reduce the moving mass of the rocker to 0.3 gram. The design process was supported by rigorous analysis, including detailed FEM and stress analysis of the flexible hinges.     

Figure  1: Complete integrated shutter mechanism with milled tita nium structure (EM, Engineering  Model). The arrow near the shutter-blade indi cates the displacement direction for the 1.5-mm  movement. 

   NASA/CP-2010-216272
337 Material Selection and Manufacturing Aspects 

A large variety of materials is available for flexible hinges. Properties like material density, Young's modulus, endurance strength, thermal conductivity and manufacturability have to be considered carefully for each application. For MERTIS, different materials like copper-beryllium alloys (e.g., CuBe 2),  martensitic steels, and titanium alloys have been tr aded. The combination of high fatigue strength and low  density made titanium Ti6Al4V the material of c hoice. The maximum Von Mises stress in the shutter  structure is 132 MPa, which is well below the limit of 350 MPa at 0.5 x 109 cycles for Ti6Al4V [2].   The dominant design driver for the hardware r ealization was the manufacturability of the 80- μm-thick  titanium hinges with a reproducible quality. Basically , there are two possible ways for the implementation:   A setup where separate components and materials like hinges, shutter-blade and support  structure are assembled together.   An integral, monolithic approach where hing es, shutter-blade and support structure are  manufactured in a single process and from a single piece of raw material.   The chosen integral, monolithic design offers the important advantage that deformations due to different coefficients of thermal expansion can be avoided and that no adjustment is required after the manufacturing. However, taking into account the required flexible hinge thickness of 80 μm (result of the  FEM-Simulation), the challenge for the hardware manufacture becomes apparent.  Indeed, the manufacturing of the very thin monolithi c structure with the sophisticated mounting of the  rocker caused most of the difficulties.  In a first run, the structure was manufactured by wire-cut EDM (Electrical Discharge Machining). The  result was not satisfying due to the heat induced surface changes during the machining. One influence  was visible as annealing colors on the titanium struct ure. Furthermore, the high affinity of titanium to  oxygen in combination with high local EDM-processing temperature resulted in the formation of titanium  oxides and an oxygen-enriched surfac e layer on the substrate (so called α-case layer, see Figure  3). The  presence of such a layer promotes cra ck formation under loading conditions.    The resulting spring constant of the flexible hinges varied by more than factor 2 (see table in Figure 2).  

 Figure 2: EDM-processed shutter sample structure (l eft) and variation of the spring constants of  three EDM-machined samples (right). 

Due to the strong variation of the spring constant s, the EDM-process has to be judged as being not  practical for the MERTIS shutter. The negative (the rmal) influence of EDM machining on the fatigue  behavior of Ti-alloys has been observed by several other authors. An antiquat ed, but still excellent  overview is given in MIL-HDBK-697A [3].   NASA/CP-2010-216272
338   Figure  3: Micrograph of the Micro-milled (righ t) and EDM-processed (below) shutter structure. 

 A new manufacturing approach was selected and the shutter mechanical part was optimized for micromilling instead of EDM ma chining. Through the ap plication of dedicated cutting parameters, the  generation of heat in the device was effectively reduced. Due to a lower the power consumption the spring constant was designed to 39 N/m.   

Figure  4: Micro-milled and passivated shutter structure.   Despite the demanding and sensitive manufacturing to lerances, the spring charac teristics of the micromachined shutters had a variance below ±1 N/m, which indicates a good reproducibility.  An unwanted result of the micro-milling process is th e generation of burrs that are formed on the material  edges. These burrs have shall be removed for fracture  prevention, fatigue resistance, or the danger of  flaking particulates. The burrs were eliminated by chemical deburring, i.e., an acid pickling procedure. Besides deburring, the pickling process was also used to tune the spring constants to their nominal values. The final step was a metallographic analysis and microscopic inspection of the structure and  especially the surface.  The chemicals which have been used for pickling are free of nitrate, produce no hydrogen when applied  (prevents hydrogen embrittlement), and the material removal is about several µm/min. The process works  NASA/CP-2010-216272
339 at ambient temperature and leaves a smooth silvery, passivated surface finish on the shutter structure  (see Figure 2) . 

Table 2: Variation of the spring constants of f our, micro-milled and chemical processed shutter  samples. The final, nominal values is 39 N/m ± 8 N/m.      Initial spring const. after micro-mach. After pickling process  Sample #4 76.8 N/m 36.1 N/m  Sample #5 76.0 N/m 37.6 N/m  Sample #6 77.04 N/m 37.97 N/m  Sample #7 75.95 N/m 36.24 N/m 

The assembled mechanism (as shown in Figure 1) is currently in life testing and further environmental tests. Tale 3 summarizes the actual performance of the shutter engineering model.   Table 3: Intermediate results of the shutter development . 

 Requirement Result for the EM  Mass 25 g 13 g  Max. dimensions 20 x 40 x 5 mm3 20 x 38 x 4 mm3  Max. Frequency 10 Hz 130 Hz  Duty cycle 1:10  compliant  Lifetime test 100 x 106 cycles in progress  Fail safe position Shutter-blade in open position compliant  Aperture 1.5 mm x 8 mm compliant 

Vibration and Lifetime Testing 

Extensive mechanical load tests have been performed. The selected maximum load level of 53 g RMS was about 150% above the nominal load.   The test criteria were:   no deformation on the flexible  hinges or structure,    no performance degradation and    no failures in microscopic inspection. 

The shutter EM showed neither degradation nor any other failure after the mechanical load test.   After the vibration test, accelerated life testing is currently in work to verify the lifetime performance of the shutter. Currently over 90 million cycles have been processed without any change of the initial shutter  parameters.    NASA/CP-2010-216272