Investigation of tape flexures for space borne deployable structures

Abstract

Space exploration arises the demand for launching large size structures to satisfy the need of high bandwidth telecommunication, earth observation and deep space interplanetary missions. Launching of these monolithic structures of sizes 3 m or more are not feasible due to limited launch fairing space of state-of-the-art launch vehicles. Therefore, the development of innovative deployment mechanisms is need of the hour. Deployment process of space borne deployable systems is the process of transition from mechanism to structure which is one of the unreliable stage due to existence of many conventional rotary joints which causes loss of energy due to backlash, friction and misalignment. An investigation study is presented in this paper for churning out a solution of flexible hinges using tape springs in state-of-the-art space deployable configurations which eliminates the factors causing loss of energy. Analytical and experimental methods are evaluated for investigating the bending behaviour of tape flexures. Tape flexures demonstrate to be a suitable candidate for compliant deployable configuration. The proposed configuration with combination of two tape flexures mounted in such a way that concave curve of each tape faces each other are structurally analysed for desired rotation angle. A comparison study is carried out for various material options of single and double layered tape flexures proposed for a flexure hinge. Practical feasibility of the proposed configuration is also demonstrated successfully on space borne deployable structures.

Keywords

Deployable antenna reflector space compliant mechanism flexure hinges tape flexures deployable truss

Introduction

Deployable structures are used for launching large size boom structure, solar panels and space antenna reflectors¹ of the order of more than 6 m. The main requirement is to fold the structures to compact size so that it can be easily accommodated in launch vehicle’s fairing space during launching and later deployed to full configuration in space after launch. Deployable structures are useful to overcome this type of challenge. Deployable mesh antenna is the best example of research for last two decades, due to its simple configuration, high thermal stability, repeatability, ease in folding to compact size. Deployment of this type of mechanism is most vulnerable stage for the system which is intended to happen in space. If any failure in full deployment, the complete mission may be ruined. This type of failure will be considered as single point failure. During the stages of deployment, actuation power need to overcome the energy losses due to friction, backlash and misalignment. To eliminate this problem, a solution of flexure based joints is proposed and investigated in this paper. Flexure based joints consists of flexible joints which are folded elastically in stowed configuration. The flexible hinges can self-deploy to certain angle by releasing stored strain energy which helps in initial deployment when released from stowed configuration. Tape springs or flexures are explored for flexure based hinges targetting for space deployable truss structure. There are many advantages of tape spring based flexible hinges like easy to manufacture, easy to assemble, low mass-to-deployed-stiffness ratio, zero friction and back lash, low cost, compact folding in stowed configuration and self-latching capability at fully deployed configuration, self-deploying capability using stored energy without the need of external power, highly repeatable and accurate positioning, no jamming of moving parts due to long term storage and adverse environment conditions. On the other side, most commonly used deployment mechanisms require actuators, motors and accessories such as latch and spring for their working. These advantages of tape flexures promote its use in deployment mechanisms. A major disadvantage is that tape spring has low stiffness in folded configuration which can cause uncertainties when tested on ground. Therefore, ground deployment testing is recommended with suitable gravity compensation. Furthermore, they also show different highly non-linear behaviour when loaded in different configurations. Therefore, it is necessary to investigate the bending behaviour of tape flexures for equal and opposite sense bending for the applications of space deployable structures. Various configurations of Tape flexures are analysed analytically and experimentally for large deflection bending with various material options. The tape flexure based hinges design has potential applications of space deployable antenna truss structures, solar arrays² and deployable booms for future Indian space missions.

Problem description

The complexity in the analysis of tape springs arises due the presence of initial transverse curvature and thin structure. Tape springs show highly varying and non-linear mechanical behaviour when subjected to equal and opposite sense of loading. In the most direct application of tape spring as hinges, the tape springs are folded for stowing purpose and is required to be released for deployment. Curved tape springs show added advantages in enhanced rigidity in fully deployed configuration which satisfies the stiffness requirement for a deployable truss structure and provides spring stiffness when folded in stowed configuration which helps in releasing from stowed to deployed configuration. Although the moment-rotation behaviours and deployment dynamics of tape springs are well known, the behaviours when folded in a truss structure are to be evaluated. Tape springs when stowed and folded to form compact structures results in formation of the fold and its interaction with the fixed support which exposes the fold area to stress concentration. Therefore, the strain analysis of the fold becomes critical and is required to be carried out. Combination of tape flexures is also required to be explored for making the compliant truss structure.

Tape flexures

Geometry of tape flexures

The tape flexures are thin shell structural member having simple uniform curved geometry which are flexible enough to produce desired motion as in conventional hinges and stiff enough to maintain structural stiffness in fully deployed configuration.³ Material of strips could be of low modulus of elasticity for providing flexibility during folding sequence and hardened to gain flexure strength to produce bending greater than 90° without having permanent deformation. The curve portion helps in maintaining stiffness in straight unfolding configuration. Best example of these tape flexures are steel tapes or carpenter tape used for measurement. Alternate material options in term of better flexibility and structural stiffness are Be-Cu alloy, CFRP with flexible resin,⁴ Ni36CrTiAl alloy.⁵ Cross-sectional profile of tape flexures is shown in Figure 1.

Bending behaviour of tape flexures

Buckling behaviour of tape flexure⁶ behaves differently when bending moment is applied on equal or opposite sense curvature as shown in Figure 2. In case of opposite sense bending, the flexure shows the higher rigidity initially, then its stiffness suddenly breaks down with a snap. It forms an elastic bend when loaded further, it reaches to a critical moment after which bending moment drops down and stabilises thereafter. When tape flexure subjects to a bending moment applied on concave curvature side which is known as equal sense bending, it shows lower rigidity and perform an elastic bend with maximum bending moment lesser as compared to opposite sense bending. Opposite sense bending produces tensile stresses along the longitudinal edges while equal sense bending produces compressive stresses along the longitudinal edges. Therefore, combination of tape spring with opposite curvature will result into smooth bending and provide adequate stiffness. This makes it a potential candidate to explore for large deflection hinges.

Wüst,⁷ Rimrott⁸ and Mansfield⁹ determined the relation between the bending moment and corresponding change in longitudinal curvature using different methodologies to understand the Moment-Rotation characteristics. The M-θ plots gives the overview of the non-linearity in the behaviour and the hysteresis. Quasi-static nonlinear behaviour of tape flexure subjected to end moments described by Dewalque et al.² for opposite sense and equal sense bending is illustrated in Figure 3. Opposite sense bending is marked with +ve sign whereas equal sense bending is marked with −ve sign as a general convention. In opposite sense bending, starting from point ‘O’, the bending moment increases linearly up to small bending angles. As rotation angle increases, the middle portion of tape flexure flattens and bending moment continuously increases till it reaches M₊^max which is peak bending moment. If the rotation angle is increased further, the tape flexure suddenly snaps down and bending moment suddenly drops down to M₊^* as shown by orange line in Figure 3 which is due to buckling of tape flexure to form a fold. Only the middle portion of tape flexure bend to form a fold and remaining portion remains straight. Further increase in rotation angle leads to a constant bending moment M₊^* which is known as steady state or residual bending moment. During controlled unloading which is shown by green colour line in Figure 3, the bending moment remains constant to M₊^* till the meeting point on loading curve and then gradually comes down to point ‘O’ linearly. Practically, the fold will remain with a small rotation angle when unloaded fully which is due to hysteresis effect. A small amount of residual energy is stored in tape flexure strip every time a fold is formed and released with the dissipation of energy. This dissipation can be computed by difference of areas under loading and unloading curves drawn by experiments.

Similarly, in equal sense bending, the bending moment varies linearly with increase in rotation angle and reaches to M₋^max relatively which is shown by blue colour line in Figure 3. Peak bending moment in equal sense bending is much smaller than the peak bending moment in opposite sense bending. Further increase of rotation angle leads to decrease in bending moment to M₋^* which is steady state or residual bending moment. The magnitude of this bending moment will also be lesser as compared to opposite sense bending. It will remain constant for further increase in rotation angle. The unloading curve in equal sense bending will remain same to loading curve with no residual energy stored in tape flexure strips which is shown by red lines. The important points about the behaviour of Tape flexure are described as:

Maximum bending moment in opposite sense bending (M₊^max) is higher than maximum bending moment in Equal sense bending (M₋^max).

In opposite sense bending, moment decreases suddenly as tape flexure snaps with increase of bend angle and fold is formed. In case of equal sense bending, moment gradually drops at a point where the tape spring snaps.

As the bend angle further increases, moment settles down to constant value, which are much less than the maximum values of opposite sense and equal sense bending respective cases.

On recovery (unloading), fold disappears at lower angle of rotation as compared to the angle at which it appeared on loading for opposite sense bending. The moment merges suddenly with the loading curve upon recovery which shows sudden increase in stiffness, which is useful for ‘self-locking’ applications.

The unloading curve was found to be same as that of loading curve for the case of equal sense bending which give smooth bending moment while loading and unloading.

Combination of two tape springs with opposite curvature will result into smooth bending and provide higher stiffness than individual tape flexures which is useful for the application of ‘flexure hinge’ for smooth rotation and auto latching at fully straighten position.

Strain evaluation methodology

The stored strain energy during the folding and bending is an important parameter to be evaluated. It allows the designer to determine adequate passive damping to obtain necessary post-deployment stability and pointing accuracy. The strain energy in bending per unit surface area can be related to changes in curvature with neglecting the torsion.⁶

Strain energy per unit surface area,

e = \frac{D}{2} [k_{l}^{2} + k_{t}^{2} \pm 2 v k_{l} k_{t}]

(1)

Where $k_{l}$ and $k_{t}$ being the change in curvature in longitudinal and transverse directions, ν is Poisson’s ratio and D is flexure rigidity. ‘+’ sign represents equal sense bending and ‘−’ sign represents opposite sense bending in equation (1). The degree of folding can be best explained using the fold angle and also the strain energy estimation requires fold angle. The fold angle is difficult to measure directly with desired accuracy. Therefore, the following methodology was used to find the fold angle with known parameters for bending of a tape spring as cantilever beam in equal and opposite sense bending.

Strain computation using analytical method

The commonly available carpenter’s tape spring made of stainless steel is used for the experiment. Material properties of tape spring is considered as specified in Table 1 and geometric parameters are modelled using CAD software as shown by Figure 4. The geometry of tape spring is completely characterised by four parameters: Length (L), thickness (t), curve angle (α) and transverse radius of curvature (R). Measured values of these properties from carpenter’s steel tape are shown in Table 2.

Table 1.

Material properties of carpenter’s steel tape spring.

Young’s modulus, E	Poisson ratio, $v$	Mass density, ρ	Yield point strength, σ_yt
200 GPa	0.33	7850 kg/m³	1200 MPa

Table 2.

Geometric properties of tape spring.

Length, L	Thickness, t	Curve angle, α	Curvature radius, R
110 mm	0.12 mm	59.73°	14.94 mm

The experiments are performed for the tape spring kept in horizontal cantilever configuration and loaded with vertical end loads. A right angle plate is used and a scale was attached on it as shown in Figure 5. One end of tape spring is fixed using a C-clamp and the other end of the tape spring is fastened with fixture plate for mounting dead weights to simulate end force. Un-supported length of tape spring is 110 mm which is considered for calculations. Weights of 10 g each are used for mounting on the thread at free end.

As it is known that different sense of bending results different behaviour, therefore measurements are taken in two steps. In the first setup, the tape spring is kept such that the convex surface faces up. As the weights applied are in vertically downward direction, this setup corresponds to the ‘Equal sense bending’. In the Second setup, the concave surface is faced up and the loading due to weight in this case represent ‘Opposite sense bending’. The weights are applied in the interval of 5 minto ensure the stability of tape spring and the displacement of free end in the horizontal and vertical axis are measured.

From the theory of shell structures,¹⁰ the generalised Hooke’s law for a shell element is as follows

[\begin{matrix} M_{x} \\ M_{y} \\ M_{x y} \end{matrix}] = [\begin{matrix} D & v D & 0 \\ v D & D & 0 \\ 0 & 0 & D (1 - v) \end{matrix}] [\begin{matrix} k_{x} \\ k_{y} \\ k_{x y} \end{matrix}]

(2)

where,

D– Flexural rigidity of plate element = $\frac{E t^{3}}{12 (1 - v^{2})}$

$v$ – Poisson’s ratio

E – Modulus of elasticity

M – Moment per unit length of application in particular direction mentioned in subscript

k – Change in curvature in particular direction mentioned in subscript

It is important to note that the moments shown in formulae are per unit length of application. So to obtain the total moment acting about a particular direction, it is to be multiplied by the length upon which it acts in that particular direction. Cross-section at the fold flattens upon loading which is shown by Figure 6.

The moment applied about the z axis (also shown as Neutral axis) will causes the change in longitudinal curvature of Tape spring (k_x). Let r and R be the final longitudinal curvature and initial transverse curvatures respectively. β and α be the fold angle and initial angle subtended by the cross-section respectively. For fold, the transverse curvature goes to zero as the cross-section flattens and the longitudinal curvature attains the value caused by the applied moment described by Seffen.⁶

Change in longitudinal curvature : k_{x} = \frac{1}{r} - 0 = \frac{1}{r}

(3)

Change in transverse curvature : k_{y} = 0 - (\pm \frac{1}{R}) = \mp \frac{1}{R}

(4)

Where, $+ \frac{1}{R}$ change in transverse curvature occurs for equal sense loading and the $- \frac{1}{R}$ corresponds to opposite sense loading.

From the generalised Hooke’s law for shell element applied at the fold,

Bending moment is computed as,

M = (R α) \frac{({Et}^{3})}{12 (1 - v^{2})} (\frac{1}{r} \mp v \frac{1}{R})

(5)

where, − sign corresponds to ‘Equal sense’ and + sign corresponds to ‘Opposite sense’.

Therefore, micro-strain is calculated using generalised bending equation as,

e = \frac{σ}{E} = \frac{M . y}{I . E}

(6)

where σ is bending stress, E = Young’s modulus.

As it can be seen from the equation (5), for computing bending moment, bend radius (r) along longitudinal direction is the only unknown parameter which can also be predicted by experimentation on tape spring. Various fold positions are generated by experimentation on a sample of tape spring which is fixed at one end and vertical loads are mounted on other end. It is observed that the longitudinal distance of fold remains same at all loading positions which is measured as shown by Figure 7 but fold radius keeps on changing with the load applied due to rotation of straight portions with respect to fold. With the knowledge of fold radius, micro strains induced in tape flexure is computed using equation (6).

The longitudinal distance of the fold as denoted in the figure is measured as 7 and 5 mm for equal and opposite sense loading respectively which is, in general, a function of the initial cross-section, length and also the sense of loading. It is also to be specified that the length of straight portion is measured for each loads and angle theta (θ) is computed using free end displacements. The angle Beta (β) is computed by applying trigonometry relations. The fold radius, r is computed in relation with fold angle (β) and fold longitudinal distance (a) which is shown by Figure 8. Bending Moment, bending stresses and micro-strain are computed with variation of load at free end for both equal sense and opposite sense bending which are tabulated in Table 3.

Table 3.

Calculated results.

Mass (g)	Equal sense			Opposite sense
Mass (g)	Moment (Nmm)	Stress (MPa)	Analytical microstrain	Moment (Nmm)	Stress (MPa)	Analytical microstrain
10	0	0	0	0	0	0
20	22.949	613.78	3069	12.09	323.43	1617
30	38.794	1037.55	5188	13.05	349.08	1745
40	49.373	1320.48	6602	15.93	426.04	2130
50	51.489	1377.07	6885	39.91	1067.37	5337
60	52.194	1395.93	6980	39.91	1067.37	5337
70	53.528	1431.6	7158	49.5	1323.91	6620
80	54.952	1469.7	7349	68.68	1836.97	9185
90	54.952	1469.7	7349	68.68	1836.97	9185
100	57.089	1526.85	7634	78.28	2093.5	10,468
110	57.089	1526.85	7634	88.6	2369.77	11,849
120	57.089	1526.85	7634	88.6	2369.77	11,849
130	57.089	1526.85	7634	98.29	2628.77	13,144
140	57.801	1545.9	7729	98.29	2628.77	13,144
150	57.801	1545.9	7729	98.29	2628.77	13,144

Strain measurements using strain gauge method

Electrical strain gauge in quarter bridge configuration is used to measure strain at the fold. Strain gauge is bonded on carpenter steel tape at the fold location such that it measures the normal longitudinal strain. Strain measurement on bent flexure is shown in Figure 9.

Loads are applied in steps at the free end of tape flexures and strain values are measured when attained stability. The frequency of the setup was set to 10 Hz. Strain values are very small of the order of microstrains. Measurements are taken for both equal and opposite sense bending cases as shown by screenshots in Figure 10 and microstrains are tabulated with X and Y displacements in Table 4.

Table 4.

Experimentally measured data.

Mass (g)	Equal sense			Opposite sense
Mass (g)	X displacement (mm)	Y displacement (mm)	Experimental microstrain	X displacement (mm)	Y displacement (mm)	Experimental microstrain
10	0	32.5	140	0	0	904
20	10	48	2800	2	1	1400
30	65	70	6200	3	2	1489
40	65	85	6635	8	5	1869
50	70	88	7400	45	30	5750
60	70	89	7950	60	30	9350
70	70	90	8300	65	40	11,100
80	80	92	8500	70	60	11,900
90	80	92	8700	70	60	12,400
100	90	95	8850	73	70	12,640
110	90	95	8950	73	80	12,780
120	90	95	9020	73	80	12,920
130	90	95	9100	73	90	13,031
140	100	96	9150	73	90	13,110
150	100	96	9175	73	90	13,180

Comparison of analytical strains with strain gauge measurements

Comparison between strain values obtained analytically and by strain measurement method are plotted for both equal and opposite sense bending as shown in Figures 11 and 12. Snap of tape flexure is clearly observed for opposite sense bending at 0.5 N load from the experimental strain measurement which further reaches to almost constant value. A similar observation is made in the equal sense bending also, after reaching to maximum strain which remain almost constant with further application of load.

It is also observed that there is a significant deviation in the results of experimental and analytical microstrains after certain load. After the load of 0.6 N for opposite sense loading and 0.4 N for equal sense loading, the stress at fold estimated analytically increases beyond the yield strength and thus violating the assumption of stress within the elastic limit and so the application of Hooke’s law to find the strains no longer holds true. Also as from the stress-strain curves, it is seen that beyond the elastic limit, the rate of increase in strain with reference to increase in stress is significantly higher than that in the elastic limit. So using the analytical method and finding the strains from stresses beyond the elastic limit using Hooke’s law will underestimate the true strains which is also seen in above plots. Therefore, the mean absolute error is calculated for readings within the elastic limit is found to be 9% and 19% for equal and opposite sense respectively.

Tape flexure for space deployable structures

As discussed in earlier sections, tape flexures are explored for formulation of frictionless compliant hinges because of their geometric simplicity. These tape flexures are flexible enough to produce desired motion as in conventional hinges and stiff enough to maintain structural stiffness in fully deployed configuration.³ Material of strips could be of low modulus of elasticity for providing flexibility during folding sequence and hardened to gain flexure strength to produce bending greater than 90° without having permanent deformation. Length and thickness of tape springs are also an important parameter in maintain bending moment and stiffness which is very well described by Chang et al.¹¹ The curve portion enhances the stiffness in straight configuration which will be useful in final deployed configuration. The stiffness and load carrying capacity increases with multilayers of tape springs and the combination with inverted tape flexures with curved portion facing each other is a good option with optimise stiffness and bending moment. Therefore, combined option with single and double tapes flexures on each side are explored for flexure hinge for space deployable structure.

Structural analysis

A combined set of double layer tape flexures¹² facing with opposite curvature as shown in Figure 13 are structurally analysed with rotational moments applied at ends and tangential contacts boundary conditions⁵ have been applied. Finite element model of combined set of tape flexure is shown in Figure 14. Holes on each end specifies the fastening location with rigid members. A non-linear large deflection analysis is carried out which is solved using Altair Hyperworks ‘Radioss’ explicit dynamic simulation tool considering various material options as mentioned in Table 5. Each case is analysed with tape flexure of thickness 0.12 and 100 mm length with unsupported length of 60 mm. Stresses are compared with various materials for flexure configuration considering the same bending moment to produce rotation motion of at least 90°.

Table 5.

Material properties considered for tape flexure configurations.

Material	Young’s modulus of elasticity (E), GPa	Mass density (ρ), g/cc	Poisson’s ratio (ν)	Remarks
Hardened steel	210	7.8	0.3	Carpenter steel tape
Be-Cu	131	8.96	0.3
CFRP	E11 = 294E22 = 4.9	1.8	ν₁₂ = 0.29	Five layer laminate 0°-45°-90°-45°-0°
Ni36CrTiAl	36.9	8.0	0.35

Boundary conditions

Fastening locations are rigidly connected by rigid links between adjacent tape strips on each side and further connected with rigid links with central node on each side as shown in Figure 15. The end rotational moments of 90° (1.57 rad) are applied on these central nodes along x-axis which are transferred to flexures fastening locations through rigid links. Frictional contacts are simulated with considering frictional coefficient of 0.1 between adjacent tape flexures on top and bottom side and between middles tape flexure. At point 1, all linear motions along x, y, z axis and rotation along y and z axis are constrained. Angular velocity along x is applied as 1.57 rad/s. Similarly at point 2, Linear motion along x, y axis and rotation along y, z axis are constrained. Linear motion along z is kept free for translation motion and angular velocity along x is applied as −1.57 rad/s for direction opposite to motion on point 1. Simulation is run for 1 stime to achieve angular motion of 1.57 rad.

Large deflection analysis results

Large deflection non-linear structural analysis is carried out using Altair’s Hyperworks Radioss simulation platform. Stress profile is analysed for each case with the boundary conditions mentioned above. Stress plot of a case is shown in Figure 16. Stresses are compared for single layer and double layer tape flexures with various material options and are described by Table 6.

Table 6.

Maximum Von Mises stresses (MPa) for various tape flexure configurations.

Material	Hardened steel (carpenter steel tape)	CFRP	Be-Cu	Ni36CrTiAl
Single layer tape flexures	403.5	82.6	196.5	90.1
Double layer tape flexures	387.6	75.6	165.1	85.6

Applications of tape flexures as flexure hinge

As discussed in earlier sections, tape flexures are explored for flexible joints of space deployable structures. Flexibility and rigidity of tape flexures are demonstrated analytically as well as experimentally. It is investigated that the combination of inverted double layer tape flexures is a best suitable option, meeting the criteria of stiffness as well as rigidity. The concept of tape flexure based hinge using steel tape is demonstrated for deployment of a boom and unfurlable antenna truss structure as shown in Figure 17. The deployable boom is a 1.5 m straight tubular section which is folded with flexure hinge and when released from folded configuration, it is deployed to straight configuration maintaining the rigidity of joint. Similarly, joint of a deployable reflector is modified to accommodate double layer tape flexures in place of conventional hinge. It is observed that the configuration with single layer flexures are deflecting with the tension loads produced by RF mesh whereas double layer flexures are well capable to accommodate mesh stretching tension loads and behave as a stable joint in fully deployed configuration which further eliminates the additional locking requirement. The configuration shown in Figure 18 in folding state is achieved fully by bending of flexures near to 90° and flexure rotational stiffness helped in initial deployment of 10°–15°.

Advantages of tape flexures in deployable configuration

Conventional joints have stiffness in both radial and tangential axis of deployed antenna reflector whereas in case of compliant joints, equal or more stiffness can be achieved by combination of tape spring configurations and number of layers. Compliant joints are frictionless joints as compared to the conventional joints which have friction between mating parts. There is no chance of loss of energy in compliant configuration due to frictional motion. Therefore, chances of obstruction to deployment is eliminated. Compliant joints are easy to manufacture and assemble as compared to multi parts configuration of conventional joints. Auto locking/latching is achieved in compliant joints by its geometry as an added advantage whereas additional locking mechanism is required in case of configuration with conventional joints. Torsion springs are required in conventional hinges to generate initial torsional moment whereas initial bending configuration of tape flexures will itself behave like a spring to produce required torsional moment which eliminates the requirement of additional torsional springs, thus providing self-deployment using strain energy.

Conclusion

This paper has addressed the criticality of deployment of a space deployable structure. To solve the problem, a solution is proposed to adapt compliant configuration of deployable reflector by replacing conventional hinges into flexure hinges. Tape flexures are investigated thoroughly as a prominent option for flexible hinges. Buckling behaviour of curved tapes are studied analytically and experimentally with strain measurement. Strain values are computed and compared with experimental results for both equal sense and opposite sense bending cases. Analytical method predicts the strain energy with significant accuracy up to a certain load, afterwards the flexure snaps with sudden drop of bending moment and value of strain start deviating from experimental values. The reason of deviation at higher loads is the stress at the fold crossing the yield strength and thus violating the ‘within elastic limit’ assumption of the analytical method. Therefore, the mean absolute error when calculated for readings within the elastic limit is found to be 9% and 19% for equal and opposite sense respectively. It is also observed that the opposite sense bending shows lesser stress and strain and higher stiffness before snap occurs and stresses suddenly rise after snap as compared to equal sense bending. Also, the load at which snap and fold formation occurs is higher in opposite sense. Therefore, combination of equal and opposite sense cases is considered for evaluation for a flexible hinge. The combinations with single and double layer of tapes are structurally analysed with various material options and found that flexible tapes made of CFRP material and Ni36CrTiAl alloy are more suitable with benign stresses under maximum rotational moment. Practical feasibility of the concept is demonstrated with modified design of joints incorporating tape flexures. Tape flexures are examined analytically and demonstrated as one of prominent option for deployable configuration which are required to be explored further for qualification for the application of space borne structures.

Footnotes

Acknowledgements

Authors acknowledge and express sincere thanks towards SAC administration for their valuable support in completion of this work.

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work is a part of PhD dissertation carried out at IIT Delhi, India in consultation and support of Space Applications Centre (SAC)-ISRO, Ahmedabad, India.

ORCID iDs

Hemant Arora

Rutvik Dangarwala

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