structural analysis and validation of a smart...

Computer-Aided Civil and Infrastructure Engineering 00 (2013) 1–15

Structural Analysis and Validation of a SmartPantograph Mast Concept

Branko Glisic*, Sigrid Adriaenssens & Peter Szerzo

Department of Civil and Environmental Engineering, Princeton University, Princeton, NJ, USA

Abstract: To progress the development of deployable,lightweight infrastructure for relief and recovery effortsin the aftermath of natural and man-made disasters, thisarticle develops a proof of concept for a smart mast thatleverages the versatility of pantograph systems and ad-vances in sensor, actuator, and informatics technologies.More specifically the article addresses key design crite-ria of transportability, deployability, global stability, andsite responsiveness through the development of analyt-ical expressions and control framework, and reduced-scale physical model testing. The case study, a three-tiered tetrahedral mast is composed of three connectedsets of planar pantograph systems and deployed by singleactuator located between two of the three mast supports.The article discusses the optimum configurations for theindividual design criteria and trade-offs to be made be-tween compactness, overturning, and operational power.The design, construction, and experimentation with a 73-cm tall fully deployed physical model reinforce the feasi-bility of the presented smart mast concept.

1 INTRODUCTION

The occurrence of extreme natural and man-made dis-asters in densely populated areas shows the need toimprove relief and recovery infrastructure. Adaptableinfrastructure that is compact and rapidly deployed inthe field is critical for an effective humanitarian re-sponse. For example wind turbines mounted on a de-ployable mast can provide a vital energy supply systemwhile functioning independently of a damaged or inad-equate existing electricity grid. The deployability andcompatibility exhibited in systems such as the “Powerin a Box” design (Peters, 2012) with its telescoping mastand top mounted wind turbines (shown in Figure 1) hasbeen a point of reference for this article.

*To whom correspondence should be addressed. E-mail:[email protected].

Typical masts that support wind turbines have a verynarrow body braced by guy lines. This system has twomajor disadvantages in a disaster relief context: (1) themast’s height is fixed and mostly limited by dead loadand the maximum wind speed; as a consequence themast cannot adapt its shape to tap into the desirablewind speeds available at varying heights; and (2) the an-choring distance of the guy lines is typically in the orderof 65% of the mast height (Ghodrati, 2002). Althoughthe mast might be very slender its bracing system takesup a large part of a site that might not be available inthe context of a dense damaged urban fabric. In sum-mary, the main challenges related to the use of mastswith turbines in urban areas struck by disaster are trans-portability, rapid deployability, responsiveness (adapt-ability), and global stability. A compact, adaptive, andstable mast can be a good solution addressing all thesechallenges.

This article gives a proof of concept through thedevelopment and exploration of analytical expressionsand a physical model of a smart pantograph mast thatdoes not impinge upon the surrounding area and thatchanges its shape in reaction to varying external stimuli.

1.1 Overview of civil smart and pantograph structures

Systems equipped with sensors, actuators, and process-ing capabilities that actively adapt to changing exter-nal conditions (such as loading) have been described assmart, adaptive, or active (Ching et al., 2008). The de-sign and analysis of smart structures is particularly ad-vanced in the aerospace and space technology sector,for example, morphing wings (Moorhouse et al., 2006),deployable space structures (Jiang-Pin and Dong-Xu,2010), etc. This article focuses on smart civil struc-tural engineering systems where although several stud-ies were undertaken (e.g., Del Grosso and Basso, 2011)less real applications exist, mostly limited to the use of

C© 2013 Computer-Aided Civil and Infrastructure Engineering.DOI: 10.1111/mice.12013

2 Glisic, Adriaenssens & Szerzo

Fig. 1. (Left) Physical model; (middle and right) full-scale prototype for “Power in a Box,” a telescoping mast with a wind turbinemounted on a transportable standard steel shipping container (“Power in a Box,” Princeton University; middle photo courtesy of

Catherine Peters; right photo courtesy of Frank Wojciechowski).

semiactive or active control devices in earthquake engi-neering (e.g., Bitaraf et al., 2012, Aldemir, 2010).

The term kinetic architecture was pioneered into thestructural engineering domain by Zuk and Clark (1970).They introduced the concept of biomimetic smart struc-tures that fold, expand, and contract to adjust to chang-ing spatial requirements. Initial research on active struc-tural control in tall building design by Yao (1972) isimportant in the context of this article. His work hintedat how tall smart buildings/masts could adapt their be-havior in reaction to external variations in loading. Thisresponsiveness presents an opportunity to keep allstructural behavior with the limit state criteria but alsoto actively change geometry to avoid, deflect, or attractmore external loading stimuli.

The recent advent of new sensor and actuator tech-nologies combined with the advances in structurallightweight design and increased computational capac-ity creates a favorable climate for the development ofsmart civil structures. The main research and industrialsmart structural design endeavors undertaken recentlyare reported as follows. Pawlowski and Holnikci-Szulc(2004) designed and tested a sensor equipped struc-ture that detects impact under extreme loads and redis-tributes internal loading. Hunt et al. (2009) developed adesign tool that generates structural systems that varylocal stiffness to globally counteract the effect of un-expected loads. Noak et al. (2006) experimentally in-tegrated actuators in trussed beams and achieved in-creasing spans and load bearing capacity. Adriaenssensand Ney (2007) advocated integrating the actuator as astructural element in realized mobile vehicular bridges.Saleh and Adeli (1998) explored the algorithms for

control of adaptable smart structures, while Kim andAdeli developed and tested various robust algorithmsfor structural control based on advanced statistical andanalytical methods (e.g., Kim and Adeli, 2004, 2005a,b). Most recently active tensegrity systems have beenresearched that use control of self-stress to actively ma-nipulate their static and dynamic behavior (Adam andSmith, 2008).

As pantograph or scissor-hinged systems can beequipped with active elements, they have the poten-tial to adapt to their environment. A recent in-depthoverview of pantograph systems is given in Thrall(2011). Pantographs are a specific type of deployablestructures that deploy from a small compact state toanother one while carrying loads. Gantes (2001) de-fined four categories of deployable structures: (1) as-semblies of one-dimensional rigid bars that form a pan-tograph (also called linkage or scissor element), (2)assemblies of rigid two-dimensional plates, (3) tensilestructures (including cable, membrane, and pneumaticsystems), and (4) tensegrity structures (assemblies ofnontouching compression struts surrounded by a tensilenetwork). This article focuses on the first category andmore specifically the pantograph mast.

A pantograph or scissor-like element consists of threenoded rigid bars (two nodes at the ends and one lo-cated between them) that are connected at their endsand at the intermediate node with a hinge. The panto-graph system, initially conceived as an accurate draft-ing tool to scale line drawings, allows for significant de-creases in height with increasing spans. When flat, thepantograph lattice (like a garden trellis) with its hingedconnections is a mechanism with one degree of freedom.

Structural analysis and validation of a smart pantograph mast concept 3

If the lattice members are totally rigid and connectedwith frictionless joints, the movement of one memberparallel to another causes sympathetic movement in theentire lattice. The first sketches of pantograph systemsappear in Leonardo Da Vinci’s 15th century notebooks(Escrig, 2001). Pinero (1965) patented the first three-dimensional deployable pantograph structure coveringa medium span performance area. Based on Pinero’sdesign, Zeigler (1976) arranged the same structuralelements in a specific spherical, dome-like configura-tion that self-locks upon full deployment. Escrig (1985)developed a series of expandable space frames usingpantographs and realized them as deployable sunroofscovering swimming pools. Both Pinero and Escrig usedsimple scissor elements: a pantograph with straight rodsconnected at an intermediate hinge. Studies that ex-amine the main principles, the geometric properties,and the shape limitations of both planar and spatialstructures made of pantograph elements with equallength beam and a centrally located intermediate hinge,have been carried out by Zhao et al. (2009, 2011) andCai et al. (2012). Hoberman’s (1990) patent describesan angulated element as building block of a hoop as-sembly. This element, realized in Iris Dome at theGerman Pavilion at the Expo 2000 Hanover, featuresidentical kinked rods rather than straight rods. You andPellegrino (1997) developed from this angulated ele-ment the generalized angulated element, an assembly ofkinked rods, which when deployed embrace a constantangle. Pellegrino and Kwan (1991) and Kwan (2003)presented numerical simulations and a physical proto-type of a pantograph mast, activated and stiffened by anetwork of cable segments and active cables. More re-cently Tan and Pellegrino presented a dynamic modelfor this cable-stiffened pantograph mast (Tan andPellegrino, 2008). Formulations that describe the dy-namic deployment equations of a pantograph mast weredeveloped by Chen et al. (2002).

Applications and research of pantograph systems thatchange shape in reaction to external stimuli are few,small scale, and found outside the domain of civilstructures in (1) high-speed transportation equippedwith active dynamics control (Park et al., 2003), (2)artificial-legged auto-motion (Kar, 2003; Freedman,1991), and (3) hand controllers for tele-operation (Longand Collins, 1992). To the best of the authors’ knowl-edge, no smart tetrahedral pantograph structures undergravity and lateral loading have been researched, de-signed, and validated with a physical model.

1.2 Scope and design methodology

The overall aim of this research is to study a deploy-able, adaptable tetrahedral pantograph mast (in short

smart mast) supporting wind turbines, to understand itsstructural and kinematic behavior and identify designchallenges. As the mast is not designed to be deeplyanchored to the soil, strong wind loading can affect itsglobal stability. This phenomenon can be avoided by de-signing the mast to change its shape (i.e., to collapseto the lowest acceptable height that would guaranteeglobal stability), while still enabling energy harvesting(by keeping the turbines in the wind).

The smart mast exhibits complex structural behav-ior. To achieve the overall aim of the project a step-by-step approach is adopted. The major fundamental ques-tions on feasibility of such a structure and the proof ofconcept are addressed in this article (Step 1). This in-cludes the studies on the change of shape under externalinfluences, overall global stability requirements, struc-tural analysis of the mast during the deployment, and aphysical concept validation. Other aspects (e.g., detailedglobal stability under the wind, realization of details,power consumption, etc.) are considered as challengesimposed by realistic conditions at application level, andthey will be addressed in future research (Step 2). Thisarticle thus presents the conceptual design and reduced-scale physical model validation of a smart pantographmast supporting wind turbines that adapts its shapein response to the presence of the predominant windspeed. At this stage of the research, detailed dynamicanalysis of the mast behavior, testing of the model inwind tunnel, and development of detailed algorithmsfor data analysis are considered as out of scope of thearticle. Based on the encouraging outcomes of the pre-sented research, these matters are rather considered asthe next stage in the research.

To keep the costs of the model minimal, the small-scale smart mast was equipped at different levels within-house available fiber-optic (FO) temperature sen-sors, instead of wind pressure sensors. Applying hot airof a certain temperature to one of the sensors causesthe mast to collapse to the exact height where the tem-perature increase occurred. The application of hot airsimulates the application of the predominant wind thatwould occur in reality. This simplification does not af-fect the results or the conclusions of the presentedresearch, since the numerical outputs are the samefor temperature and wind pressure sensors (i.e., scalarvalue for each instrumented point). Once the proof ofthe concept is established in this article, more sophisti-cated sensing systems for the mast could be designedbased not only on FO pressure sensors (Pinet et al.,2007), but also on FO strain or displacement sensors(Glisic et al., 2007; Inaudi et al., 2001). The preferencefor FO sensors is based on their proven accuracy, res-olution, versatility, and long-term stability (Inaudi andGlisic, 2002, 2006; Glisic and Inaudi, 1999).


Fig. 2. Conceptual rendering of the three-dimensionaltetrahedral pantograph mast.

2 CONCEPTUAL DESIGN OF THEPANTOGRAPH MAST

2.1 Geometrical properties

In this section, the kinematic analytical concept of thedeployable mast is presented. The three-dimensionaltetrahedral mast is assembled of three inclined two-dimensional planar pantograph systems, as shown inFigure 2.

The tetrahedral overall shape is preferred over a pris-matic shape as the former offers improved global stabil-ity against overturning (e.g., due to wind). The analyti-cal formulation that describes the geometry and morespecifically the positions of the end and intermediatenodes of the two-dimensional straight rod pantographsin all phases of shape change is presented as follows.

The planar systems are assembled into a three-dimensional mast by connecting their end nodes. Tolimit stresses on those end nodes, their hinges (indi-cated in Figure 3 by notations A, B, C, and D) must becollinear during all deployment stages. Consequently,each pantograph is symmetric with respect to the ver-tical axis as shown in Figure 3.

Any geometric deviations of the end hinges fromcollinear arrangement, increases fatigue damage in thehinges after several cycles of elongation and contractionof the mast. Analytically this required collinear geomet-ric condition is fulfilled if

cn = cn−1 = · · · = ci · · · = c1 (1)

and

li = 1 − ci−1

cili−1 =

(1 − c1

c1

)i−1

l1 (2)

Fig. 3. Schematic representation of a two-dimensional planarpantograph whose end hinges A, B, C, and D must be

collinear during the entire deployment process.

where li is the length between the two end nodes of theith scissor element, ci is the ratio of the length betweenthe bottom end node and the intermediate node to thelength between the two end nodes of the ith scissor ele-ment (i = 2, . . . n, see Figure 3).

The value of c1 must be higher than 0.5 that is, (1 −c1)/ c1 < 1. For c1 < 0.5 the overall shape of the mast isan upside-down tetrahedron, while for c1 = 0.5 the over-all shape is prismatic. Thus, for c1 > 0.5, Equation (2)describes the decreasing lengths of the scissor elementsin successive order and indicates that the portion abovethe hinge of the (i − 1)th element is equal to the portionbelow the hinge of the ith element. If the total num-ber of different elements is n, then sum of the lengthsof n different elements Ln can be calculated usingEquations (3a and b)

Ln =n∑

i=1

li =n∑

i=1

(1 − c1

c1

)i−1

l1 =1 −

(1−c1

c1

)n

1 −(

1−c1c1

) l1 (3a)

and

Ln <1

1 −(

1−c1c1

) l1 = L∞ (3b)

h = l11 − ( 1−c1

c1)n

1 − ( 1−c1c1

)

√1 − d2

c21l2

1

√1 − d2

3h2∞,d

= Ln

√1 − d2

c21l2

1

√1 − d2

3h2∞,d

,h∞,d ≥ d√3

(4)


where

h∞,d = 1

1 −(

1−c1c1

) l1

√1 − d2

c21l2

1

= c1l1

2c1 − 1

√1 − d2

c21l2

1

(5)Equation (3b) shows that, theoretically, for given

c1 > 0.5 the sum of length of elements cannot exceedsome limit value L∞, regardless of the number of ele-ments n.

It is often the combination of slightly desynchronizeddual or triple actuators that causes deviations from thepredefined geometry and sets up undesirable residualstresses in the system (Adriaenssens and Ney, 2007). Toavoid this phenomenon, the choice of pantographs assubsystems for the tetrahedral mast, is driven by the no-tion that the mast’s vertical height can be controlled bymanipulation of one degree of freedom only. This de-gree of freedom consists of the relative horizontal po-sition (indicated in Figure 3 by the notation 2d) of onesupport node with respect to the second, pinned supportnode provided the third support node is free to slidein the horizontal plane. The orientation of the displace-ment is defined by the first and second node. The use ofone single actuator that moves one support toward oraway from the second support allows for the controlledthree-dimensional movement (as the mast increases itsheight, its width becomes smaller and vice versa). Themast height h can thus be expressed in terms of the dis-tance between the two controlling support nodes 2d, thenumber of scissors n, the ratio of the length betweenthe bottom end node and the intermediate node to thelength between the two end nodes c1, and the length be-tween the two end nodes of the bottom scissor elementl1, as shown in Equations (4) and (5).

Equation (5) represents the height of the triangle in-scribed by the two-dimensional pantograph system (tri-angle formed by line ABCD, the base of the panto-graph, and the line connecting the middle hinges). Thefirst square root term in Equation (4) is the sine of theangle formed by the pantograph members with the two-dimensional base, and the second square root accountsfor the tilting of a pantograph plane three dimension-ally. Equations (3) and (4) point that for given Ln andn, the variables l1 and c1 cannot be independently se-lected, that is, they depend on each other.

The theoretical predefined maximum height of themast h will occur for d = 0, and in this case it is equalto Ln, that is, h(d = 0) = Ln. The largest value of d isfor two-dimensional pantograph equal to c1l1, in whichcase h = 0. However, for three-dimensional tetrahe-dral pantograph, the condition that the hinges of threeplane pantographs should be connected imposes thath∞,d ≥d/

√3 (see Equation (4)). Consequently, the max-

imum dmax can be calculated from Equation (5) by solv-ing equation h∞,d = d/

√3, as shown in Equation (6)

dmax = c1l1

√3

3 + (2c1 − 1)2(6)

For a nondeployed mast, the height is minimal (i.e.,for a mathematically idealized mast the height is zero)and d = dmax. To adjust the height of the mast, the actu-ator changes the value of d. The stroke s of actuator isthen defined as follows:

s = 2dmax − 2d, smax = 2dmax (7)

For given maximum value of h (i.e., Ln, seeEquation (4), larger value of c1 (closer to 1.0) implieslarger dmax and consequently larger smax and l1 (seeEquations (3), (6), and (7)). Large values of dmax andl1 are not optimal as the footprint of the mast will belarge and the individual beams of the pantograph willbe long. When not deployed, the overall size of the mastwill be large too and not compact enough to be trans-ported (the longest length of beam l1 will be too long).In addition, a large value of smax requires a large strokeactuator. Contrary, for smaller values of c1 (closer to0.5), a nondeployed mast is very compact, and short-stroke actuator would be required. This discussionis illustrated by values for maximum element length,stroke, and height for a three-tiered tetrahedral mast inTable 1.

For example, the maximum beam length that can fitin a standard 40 ft. container is 12 m, which allows fora mast with three tiers of scissor elements and c1 =0.55 to have a maximum theoretical height of 27 m,approximately.

The relations between h and d, and h and s dependon the selection of l1 and c1, and their dependence is il-lustrated in Figure 4 for n = 3. Figures 4a and b showthat coefficient c1 does not significantly influence the re-lationship between h/Ln on one hand and d/(2c1l1) ands/(2c1l1) on the other hand.

However, the influence of the stroke on the height ofthe mast, that is, the influence of the ratio s/(2c1l1) to theratio h/Ln can be roughly divided into three intervals:

1. The first interval corresponds to s/(2c1l1) ratiochange from 0.00 to 0.05, approximately. Theseinitially small changes of stroke produce largechanges in height (h/Ln ratio changes from 0.0 to0.3, approximately). Consequently small errors instroke position can produce large errors in mastheight.

2. The second interval corresponds to s/(2c1l1) ra-tio change from 0.05 to 0.60, approximately. Thischange of stroke produces a change in h/Ln


Table 1Comparison of ratios between maximum length beam l1,maximum stroke smax and maximum theoretical height ofmast Ln for masts with three scissor elements (n = 3) and

various values of c1

Max. length of a Max. stroke of aParameter scissor beam scissor beamc1 [−] l1/Ln [−] smax /Ln [−]

0.50* 0.33 0.330.55 0.40 0.440.60 0.47 0.590.70 0.62 0.870.80 0.76 1.220.90 0.89 1.601.00† 1.00 2.00

*Prismatic mast, not included in this research.†Mast “collapsed” to hinged beams.

ratio from 0.3 to 0.9. This second stroke inter-val promises a better height control than the firststroke interval.

3. The third interval corresponds to s/(2c1l1) ratiochange from 0.60, approximately, to smax/(2c1l1).In this interval, a larger stroke is applied forvery small gain in the mast height. This intervalseems to promise the best control of the mastheight is actually not optimum for two reasons:(1) large applied stroke requires a larger actua-tor, and (2) for a larger stroke the value d be-comes very small and stability of the mast can becompromised.

In conclusion, based on the considerations above, thesecond interval seems to be the most suitable for ac-

tive operation of deployed mast. This second intervalwas chosen for exploration when validating the physicalmodel (see Section 3). Based on Table 1, the value ofc1 must be closer to 0.5 for a compact mast. However,this last requirement is in contradiction with the globalstability and structural efficiency requirement, as shownin Subsections 2.2 and 2.3, respectively.

2.2 Global stability

Exposing the mast to lateral forces produces an over-turning risk. In the preliminary study three load casesshould be considered: (1) static loads due to the self-weight of the mast and the turbine, (2) the wind load,and (3) dynamic loads due to flow-induced vibrations ofthe wind turbine. The presented structure has a verti-cal axis wind turbine with three helically swept blades,which practically eliminates the turbine’s dynamic ef-fects on the mast (i.e., the cyclic aerodynamic loading ofeach blade’s revolution) (Crosher and Cochrane, 2008).Consequently, only the first two load cases are consid-ered. The horizontal forces acting on the mast are thosegenerated by the wind pressure exerted on the turbineP (the turbine is modeled as a solid panel, and thevalue of P accounts for the dynamic amplification fac-tor) and over the body of the mast w(z) as illustrated inFigure 5a. The value of P and the distribution of w(z)are determined by the strain sensors installed on theturbine support and pressure sensors installed on themast scissor elements. Assuming that the mast is not an-chored to the soil, the only force opposing the overturn-ing is resultant M + T that combines the weights of themast M and turbine T (T≈ 5–20% of M depending onmaterial and size).

Fig. 4. (a) Relation between the relative height of the mast h and position d of the movable node for n = 3 and various values ofcoefficient c1; (b) influence of the actuator stroke s to h for n = 3 and various values of c1.


Fig. 5. (a) Simplified analysis of forces acting on mast and (b) adaptation to external forces improves stability.

By changing the height of the mast, two parametersare changed: (1) the wind load and the associated over-turning moment are decreased, and (2) the footprint ofthe base is increased and consequently the resistance tooverturning is improved as shown in Figure 5b.

The aim of this section is to assess how the coefficientc1 influences the global stability of the mast. To sim-plify the presentation the influence of the wind blow-ing on the body of the mast, this load is replaced by itsresultant W (multiplied with dynamic amplification fac-tor Aw) acting at the centroid of the load, that is, at theheight hw. Values of W and hw are thus calculated asfollows:

W = Aw

∫ h

0w(z)dz and hw = Aw

∫ h0 w(z)zdz

W(8)

To oppose the overturning the global moment due tothe weight of the mast should not be smaller than themoment generated by the wind, that is

Ph + W hw ≤ (M + T )d

√3

3(9)

Rearranging Equation (9) and combining with Equa-tions (3) and (4) leads to

F

G≤ d

h

√3

3= (2c1 − 1)

√3

3d

c1l1(1 −

(1−c1

c1

)n) √1 − d2

c21l2

1

√1 − d2

3h2∞,d

(10)

where F = P + Whw/h is equivalent overturning forceat the top of the mast calculated using sensor measure-ments and G = M + T is total weight of the mast andturbine combined. This equation is used in control soft-ware algorithms to evaluate stability conditions of themast.

The relationship between the upper limit of ratio F/Gand value d and stroke s is given in Figures 6 and 7.

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Upp

er li

mit

for

F/G

[-]

d/(c1l1) [-]

F/G (c1=0.55)

F/G (c1=0.60)

F/G (c1=0.70)

F/G (c1=0.80)

F/G (c1=0.90)

Fig. 6. Relation between F/G ratio and d.

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Upp

er li

mit

for

F/G

[-]

s/(2c1l1) [-]

F/G (c1=0.55)

F/G (c1=0.90)

Fig. 7. Relation between F/G ratio and stroke s.

Figures 6 and 7 show that more stability is achievedif the value of c1 is closer to 1.00. For example, assum-ing that two masts have the same weight, for a givenstroke s the mast with c1 = 0.90 will allow several times


a higher wind force on the turbine than the other onewith c1 = 0.55 (see Figure 7). An additional conclusionfrom Figure 7 is that an excessively large stroke will de-crease stability of the mast, thus the stroke should bekept out of the third interval (see Subsection 2.1).

In conclusion, for global stability sake c1 should becloser to 1.00. This finding is in contradiction with thecompactness and controllability requirements that fa-vor a short stroke (see Section 2.1). However, Equation(8) shows that by increasing the weight G of the mastit is possible to increase the stability against overturn-ing and to allow for larger horizontal wind forces. In thecase of a smart mast mounted on a steel shipping con-tainer (as the “Power in a Box” project) the mast can beadditionally stabilized (its weight artificially increased)by the container in which the mast was transported andmounted (the weight of a 40’ steel shipping container is38 kN).

During folding and unfolding of the mast, the globalstiffness of structure changes due to the overall changein geometrical shape. Although this change influencesthe displacement distribution along the mast, it does notaffect the global stability of the structure, which onlydepends on parameters used in Equations (9) and (10).

2.3 Simplified structural analysis

The aim of this section is to analyze the relationship be-tween the internal forces, the ratio c1, the values of d,and stroke s. For the purpose of this preliminary designanalysis, the load acting on the mast is divided into avertical component (due to dead load and wind suction)and horizontal component due to wind. For each of thethree pantograph systems the load can further be splitinto in-plane load (acting in the plane of pantograph)and out-of-plane load (acting perpendicular to the planeof pantograph). A detailed analysis of all loading com-binations exceeds the scope of this section. To simplifythe presentation, without reducing the validity of thegeneral conclusions, only the analysis of internal forcesgenerated by in-plane dead load is presented in detail.In the other load cases results leading to similar con-clusions are obtained. In the analysis the pivot and endconnections are assumed to be frictionless pins. Mod-eling of the friction in the joints is out of the scope ofthis study. The friction in the joints is found to amplifythe horizontal forces for about 25% (e.g., Gantes et al.,1993). In the study of the full-scale prototype, it is as-sumed that the horizontal forces can be amplified by afactor of 1.25.

Each pantograph-tiered system is statically determi-nate in its plane and the loads flow from the top tothe bottom. More precisely the load from the upperscissor element is transmitted to lower scissor element.

Fig. 8. Analysis of in-plane forces in ith element.

In addition the dead load is symmetric producing sym-metric influences in two beams of the scissor element,and the vertical force in the hinge is equal to zero. As-suming perfect symmetry in dead load and in the pan-tograph’s geometrical and mechanical properties, thein-plane load acting on the ith scissor element of a pan-tograph is transmitted only to the i − 1st element of thesame pantograph without affecting the other two pan-tographs in the tetrahedron. In-plane loads acting on ithscissor element are shown in Figure 8.

As the flow of the forces is from upper to lower scis-sors, the forces transmitted from the ith to i − 1st scissorelement are calculated using the following recursive for-mulas obtained from the equations of equilibrium

VIP,i−1 = VIP,i + qIP,i li (11a)

HIP,i−1 =(

1 − c1

c1

)HIP,i + 1

c1

dc1l1√

1 −(

dc1l1

)2VIP,i

+ 12c1

dc1l1√

1 −(

dc1l1

)2qIP,i li

(11b)

where di/li is substituted with d/l1 (see Figure 2), i = 1 ton, and index IP indicates in-plane load.

The recursive Equations (11a and b) can be rear-ranged as follows:

VIP,i = VIP,n +n∑

j=i+1

qIP, j l j (12a)


and

HIP,i =(

1 − c1

c1

)n−i

HIP,n

+ 1c1

dc1l1√

1 −(

dc1l1

)2

(1−c1

c1

)n−i− 1(

1−c1c1

)− 1

VIP,n

+ 1c1

dc1l1√

1 −(

dc1l1

)2

n−i−1∑m=1

(1−c1

c1

)m− 1(

1−c1c1

)− 1

qIP,i+m+1li+m+1

+ 12c1

dc1l1√

1 −(

dc1l1

)2

n−i∑m=1

(1 − c1

c1

)m−1

qIP,i+mli+m

(12b)

where i = 0 to n − 1.Finally for dead load only, that is, HIP,n = 0, constant

value of distributed load, that is, qi = qIP = constant,and taking into account that in-plane load changes asthe inclination of the pantograph changes with the pa-rameter d (or stroke s, see also Equation (5)), Equation(12) transforms to

VIP,i =√

1 − d2

3h2∞,d

⎛⎝Vn + q

n∑j=i+1

l j

⎞⎠ (13a)

where VIP,n = Vn

√1 − d2

3h2∞,d

, qIP = q√

1 − d2

3h2∞,d

and

HIP,i =

1c1

dc1l1

√1 − d2

3h2∞,d√

1 −(

dc1l1

)2

(1−c1

c1

)n−i− 1(

1−c1c1

)− 1

Vn+

1c1

dc1l1

√1 − d2

3h2∞,d√

1 −(

dc1l1

)2

⎡⎢⎣

(1−c1

c1

)n−i−

(1−c1

c1

)(

1−c1c1

)2− 1

+ 2

⎤⎥⎦ q Ln

(13b)Equation (13a) shows that the “vertical” in-plane

force is minimal for i = n (at the top of the mast) andgradually increases from the top to the bottom of themast where it is maximum (i = 0, at the base). Equa-tion (13b) shows that similar applies for the horizontalforce. In Equations (12a and b), Vn corresponds to theweight of the turbine and q to the linear mass of themast beams. For illustrative purposes, the relationshipbetween d and the horizontal force at the base of themast with three scissor elements (n = 3) for Vn = 0.2qLn

(weight of turbine equals 20% of the weight of the mast,similar as for the full-scale prototype, see Section 3.1)normalized with total weight (Vn + qLn) is given inFigure 9 for various values of parameter c1.

Figure 9 shows that the horizontal reaction atthe base of the mast increases with the increase

of parameter d. The horizontal reaction increasesas d approaches its maximum value (see Equa-tion (6)), and then drops to zero when the mastcollapses into a plane and reaches a critical con-figuration. The increasing horizontal reaction ismore emphasized for smaller values of parametersc1 < 0.7, especially for values d/(c1l1) > 0.85. Thisobservation is important as the horizontal support ismoved by the actuator and large horizontal reactionrequires a more powerful actuator.

Thus, during deployment, the mast cannot initially beraised from the collapsed horizontal state using the hor-izontal actuator, used to control the mast shape duringthe operation. Raising the mast from a horizontal state,needs an initial out-of-plane “kick” force. For exam-ple the actuator could temporarily be placed verticallyin the center of the mast to raise the mast to its low-est operational height. Once the mast has achieved thisheight, it can be temporarily fixed (supports temporar-ily locked) and actuator can be placed in its operationalhorizontal position. Alternatively, two “permanent” ac-tuators can be used, one to raise the mast and the otherto operate it. In this case, these two actuators will oper-ate completely independently, that is, the actuator thatraises the mast to its lowest operational height can bedisconnected once it has fulfilled its function. The useof two interchangeable actuators can also be justifiedto add redundancy to the systems (one actuator can beused for dual purpose if the other actuator fails).

For values of d/(c1l1) < 0.85, that is, during the op-eration of the mast (see Section 2.1), the horizontal re-action is not excessively high. As the value d/(c1l1) willbe higher than 0.85 only during the deployment of themast, the smaller values of c1 are acceptable, with thecompromise that the lack in efficiency of the structure iscompensated with a gain in compactness.

3 SMART TETRAHEDRAL PANTOGRAPHMAST: PHYSICAL PROOF OF CONCEPT

3.1 Initial target dimensions and performance

Based on the analysis presented in previous sections,it is possible to draft the target specifications for thesmart tetrahedral mast. As the aim of this study is toprove the concept of the smart mast, only a simplifiedfeasibility and performance assessment is made, whilethe development of design details are left for the sec-ond stage of the project. For transportation purposes,the mast should be collapsed and the mast sides dis-connected along one imaginary edge of the tetrahe-dron and “folded” along the two other imaginary edges.In this folded and collapsed configuration, the three


0.0

2.0

4.0

6.0

8.0

10.0

12.0

14.0

16.0

18.0

20.0

22.0

24.0

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

H0/(

Vn

+qL

n)[

-]

d/(c1l1) [-]

H0 (c1=0.55)

H0 (c1=0.60)

H0 (c1=0.70)

H0 (c1=0.80)

H0 (c1=0.90)

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

H0/(

Vn

+qL

n)[-

]

d/(c1l1) [-]

H0 (c1=0.55)

H0 (c1=0.60)

H0 (c1=0.70)

H0 (c1=0.80)

H0 (c1=0.90)

(a) (b)

Fig. 9. (a) Relationship between d and the horizontal force at the base of the mast with three scissor elements (n = 3) forVn = 0.2qLn normalized with total weight (Vn + qLn); (b) detail from Figure to the left.

mast sides (each containing connected scissor elements)become parallel. To fit in a standard 40’ shipping con-tainer, the size of the longest member should be de-fined so the value 2dmax does not exceed 10 m, keep-ing about 1 m space around the folded mast. Deploy-ment from this compact form can be performed man-ually, with the help of the actuator (see Section 2.3).Based on the “Power in the Box” project, the minimumoperating height is established around 10–12 m, and themaximum height around 18–20 m. The operating forcein actuators should be kept relatively small 10–50 kN(equivalent to 1–5 tons), so the actuator will not haveexcessive power requirements. The mast can be madeof thin-walled rounded rectangular steel profiles 50 ×150 × 4 mm. A vertical axis wind turbine with three he-lically swept blades, can be used, with weight of 4.5 kNand the projected peak power of 8.5 kW at wind speedof 16 m/s. Combining the drafted specifications with theresearch presented in Section 2, the initial target speci-fications are drafted as shown in Table 2.

At this stage of the research, it is difficult to accuratelyestimate the wind speed that will generate the maximumoverturning moment. Wind tunnel test will be necessaryfor this purpose. Nevertheless, for the purposes of thestudy assuming drag coefficient of 2 and uniform distri-bution of the wind along the mast height (a conserva-tive assumption), based on Equation (10), one can con-clude that the mast can support wind gusts of 26 m/s.However, the true wind pressure will be actually mea-sured by the pressure sensors (and not calculated fromthe wind speed). The control algorithms will have sev-eral criteria for adjusting the height of the mast: (1) toachieve optimal energy production efficiency, the mastwill adapt its shape to tap into the optimal wind speedrange (close to 16 m/s), (2) for the global stability, the

Table 2The target specifications of the smart mast

n/c1 [−] 3/0.55

Length l1 [m] 9Maximum theoretical height 22.4

Ln [m]Maximum operating height 20.1 = 0.90Ln

hmax [m]Minimal operating height 11.9 = 0.53Ln

hmin [m]Maximum stroke smax [m] 9.9Stroke at hmax 5.6 = 0.57(2c1l1)

s(hmax) [m] (d = 2.1 = 0.43c1l1)Stroke at hmin 1.5 = 0.15(2c1l1)

s(hmin) [m] (d = 4.2 = 0.85c1l1)Estimated weight with turbine 25 (63)

(w. 40’ container) G [kN]Max. overturning moment at hmax 53 (133)

(w. container) Mot(hmax) [kNm]Max. overturning moment at hmax 104 (264)

(w. container) Mot(hmin) [kNm]Actuator force as per Section 2.3

at hmax H0(hmax) [kN]14

Actuator force as per Section 2.3at hmin H0(hminx) [kN]

45

mast’s height will change to ensure a satisfactory safetyfactor as per Equation (10), for example, for safety fac-tor 2, F/G <(2d

√3)/(3h), and (3) to reduce the power

requirement, the actuator will move slowly and not inreal time. Its movement will be controlled by thresh-olds based on 5–10 min wind-speed and pressure statis-tical analysis (averages and dispersion, e.g., Iglewicz andHoaglin, 1993). A typical actuator speed of 1–5 m/min.(average power required 0.8–4 kW) is envisaged.


Fig. 10. (Left) View of smart mast with its control system; (upper right) detail of the scissor beam hinge; (lower right) detail ofthe inter-pantograph hinge (top view to the mast).

The actuator speed and the length of intervals forwind statistical analysis are site dependent and are de-termined based on historical data for each specific site.If the historical data show that the optimal height forthe turbine does not vary significantly over time, andthe wind gusts do not exceed the speed limit establishedfor safe functioning of the mast, then the time intervalsfor the control system may be significantly elongated.However, it is not recommended to turn the control sys-tem off to be able to act upon extreme events that wererarely registered, or not registered in the history. Inthe cases where the historical data are missing, conser-vative values will be taken (higher safety factor, shortertime intervals for statistical data analysis, and fastermovement of the actuator).

3.2 Description of the physical model

To prove the smart mast concept, a reduced-scale modelwas built and its responsiveness tested. The geometricscale of the model was adjusted to available materialand equipment, and set to 1:27.5 with respect to tar-get specifications given in Table 2. The model consistedof three two-dimensional pantographs, each made ofthree-tiered connected scissor elements that decreasein size (see Figure 10). The dimensions of the modelwere chosen based on geometrical stability and struc-tural analysis presented previously in Section 2. It iscomposed of 18 laser-cut 9-mm thick acrylic beams.As acrylic has lower density than steel, these beamsare widened and thickened to account for the concen-trated force transfer in the hinged connection at thebeam extremities and at the intermediate hinges. Eachscissor unit is made of two identical members hingedtogether using a stainless steel rotational hinge (seeFigure 10). The extremities of the different tiers of scis-

sor elements are connected with a similar type of pla-nar rotational stainless steel connection. The three pan-tographs are connected at the beam extremities usinga folded rubber hinge (see Figure 10). The resultingweight of the mast was 24 N (mass of 2,436 g). Thus,the scale of the weight with respect to target values wasapproximately 1:1,000, which was a direct consequenceof lower density of acrylic (6.6 times compared withsteel), shorter lengths, and smaller cross-section. Lowerstrength of acrylic resulted in larger area of the scis-sor elements, and thus the aerodynamics properties ofthe model would not be representative for the targetedmast. However, as the wind tunnel tests were out of thescope of this study, this matter did not affect the overallpresented results. The mast model rests on three sup-ports: the first is pinned in all directions, the second canslide along one direction (along the stroke of the actu-ator), but it cannot slide in the perpendicular direction,and the third support is free to slide in all directions. Thetwo sliding base supports displace over a Teflon coatedsurface and ensure that during displacement those sup-ports do not encounter frictional resistance and thus donot induce extra stresses in the model. Table 3 presentsthe main characteristics of the model.

3.3 Control system

The mast model is equipped with a smart control sys-tem, that is, with a sensing system, actuator, and dataprocessing subsystem shown in Figure 10.

The sensing system consists of three Fiber Bragg-grating (FBG) sensors for temperature monitoring(simplification made to use readily available material,see Subsection 1.1), reading unit, and associated in-terface software. The error limits of the system were±0.2◦C in short term and ±0.5◦C in long term. The


Table 3The main characteristics of the smart mast physical model

n/c1 [−] 3/0.55

Length l1 [mm] 327Maximum theoretical height 813

Ln [mm]Maximum operational height 736 = 0.90Ln

hmax [mm]Minimal operational height 429 = 0.53Ln

hmin [mm]Maximum stroke smax [mm] 360Stroke at hmax 207 = 0.57(2c1l1)

s(hmax) [mm] (d = 77 = 0.43c1l1)Stroke at hmin 55 = 0.15(2c1l1)

s(hmin) [mm] (d = 153 = 0.85c1l1)Weight G [N] 24Max. overturning moment at hmax 51

Mot(hmax) [Nm]Max. overturning moment at hmax 101

Mot(hmin) [Nm]Horizontal force as per Section

2.3 at hmax H0(hmax) [N]13

Horizontal force as per Section2.3 at hmin H0(hmin) [N]

43

frequency of measurements was 1 kHz. The sensorswere installed at hinges of scissor elements No. 2 and3, and at interpantograph hinge of these two scissor el-ements (see Figure 10). The acquired data were storedin the form of text-files on a central PC. Simulation ofwind pressure sensors by temperature sensors is justi-fied by the fact that the numerical outputs are the samefor both types of sensors (i.e., scalar value for each in-strumented point).

A single linear actuator provided the mast with itskinematics. The actuator has a maximum stroke of203.2 mm (8 in.), high torque 17 stepper motor, andthrust to 1.78 kN (400 lbs.), and it operates on itsown power unit. The total stroke of available actua-tor is shorter than the one required for full deployment(360 mm, see Table 3), but sufficient for the operation(operational range was 207–55 = 152 mm). The inter-face software was installed on a central PC that alsocontrols the actuator. The speed of the actuator was ad-justed to draft target value.

A MatLab-based Control Software (MathWorks,Inc., Natick, MA, USA) was created and uploaded onthe central PC. The program processes the data ac-quired by sensors, makes an analysis, and sends con-trol information to the actuator, so the latter can induceshape change of the mast. A simple Java-based routineallows for integration of various interfaces (sensors andactuator) and Control Software, and provides a fully au-

tomatic operation of the control system (sensing, pro-cessing, actuation).

A change in temperature for a minimum averageddifference of 5◦C for period not shorter than five sec-onds (statistical analysis interval, total of 5,000 measure-ments) at any location or any combination of locations(“area”) equipped with sensors (that simulates exces-sively strong wind at that location or that area) resultsin movement of the top of the mast to that location. Theidea being that the mast equipped with wind turbinesinstalled at its top would try to avoid “strong wind”over its body, still keeping the turbine in the acceptablystrong wind. The interrogation period of five secondswas set to be short so the tests can be performed quickly,by blowing, still collecting a large amount of measure-ments that are statistically analyzed. The speed of actu-ator was set to 5 mm/s, so the full movement is achievedwithin 30 seconds. With this speed no visible dynamiceffects were noticed due to actuation.

3.4 Shape changing sequence

Figure 11 illustrates how the tetrahedral pantographreduced-scale physical model responds to the externalstimulus of temperature by shifting its shape in a stablemanner. Upon sensing a change in temperature (humanbreath) at one or several sensors, the mast contractsso that its top is at the level of initial location of thelowest activated sensor. When the temperature differ-ence is removed, the mast expands to initial deployedposition.

4 CONCLUSIONS AND FUTURE WORK

This article presents progress in the field of smart civilstructures by investigating an adaptive tetrahedral pan-tograph mast with potential application in the domainof disaster relief and recovery infrastructure. Key designcriteria in this context are compactness (for transporta-tion), deployability (for ease of erection), responsive-ness (adaptability to changing and unknown externalboundary conditions such as loading), and global stabil-ity (in absence of guy lines in a restricted site).

The project has been developed in two phases, andthe first phase is presented in this article, while the sec-ond phase represents the topic of the future work. Themajor fundamental questions on feasibility of a tetra-hedral pantograph mast and the proof of concept areaddressed, including the studies on the change of shapeunder external influences, global stability requirements,structural analysis of the mast during the deployment,and a physical concept validation.


Fig. 11. Contraction and deployment sequence of the small-scale pantograph smart mast reacting to temperature differences,sensed at the element extremities.

The following are the contributions that to the bestof the authors’ knowledge have not been presented inearlier research:

1. The study considers deployable mast with a tetra-hedral global form made up of scissor elementsthat do not have intermediate pivot hinge in themiddle of the beams;

2. The kinematics of the tetrahedral mast were de-rived taking into account the change in inclina-tion of the planes of scissor elements as the mastchanges shape;

3. The structural analysis of this particular scissor el-ement is performed taking into account the changein inclination of the element plane; analytical ex-pressions are derived in closed form;

4. A simplified analysis of stability under the windload was performed, and stability criterion estab-lished taking into account the variable height ofthe mast;

5. A physical smart mast model, equipped with sen-sors and actuators, was created to prove theconcept.

Based on the case study of a tetrahedral three-tieredmast, the article derives the geometrical relationshipbased on deployability criteria between scissor beamlength on one hand and mast height and actuator strokelength on the other hand for a range of intermedi-ate hinge locations. The results of this analysis furthershow that the effect of the actuator stroke on the to-

tal height does not significantly depend on the positionof the intermediate scissor hinge. However, when de-ployed from a compact state, small changes in strokelength generate large initial increases in mast height. Ina second interval, further increases in stroke length re-sult in smaller gains in mast height. This interval is fa-vorable when exercising control over the deployment isimportant. A third stroke interval exhibits large actua-tor strokes with very small mast height increase.

Geometrically, the most compact mast requires its in-termediate hinge to be positioned close to midway be-tween the beam’s extremities. Analytical global stabilityexpressions demonstrate that this compactness ideal isin contradiction with requirements for preventing over-turning. However, the overturning can be prevented byincreasing the weight of the mast by container used forits transportation.

A structural analysis at element level investigates theflow of forces and evaluates the horizontal base com-ponent that needs to be resisted by actuator during allphases of deployment. The actuation force required tolift or to collapse the mast is of interest as it directlyrelates to the structural and operational efficiency andcost of the smart mast. As expected, the horizontal ac-tuation force increases nonlinearly as the mast lowersand approaches its maximum value just before drop-ping off to zero when attaining a theoretical horizon-tal compacted state. The increase in actuation forceis more pronounced for more compact designs (wherethe intermediate hinge is close to the middle locationof the scissor beam). For the established intermediate


favorable control stroke interval, the required actuationforce proves to be acceptable.

To validate the practical feasibility of the struc-ture, its kinematics and responsiveness, a small-scaleacrylic three-tiered prototype equipped with a smartcontrol system was designed, constructed, and exten-sively tested. Its control system consisted of (1) FOsensors with associated reading unit and interface soft-ware, (2) an actuator with associated interface soft-ware, (3) an original MatLab-based Control Softwarecreated upon the theoretical equations presented inthe article, and (4) an original Java routine that in-tegrated various interfaces and Control Software andprovided with a fully automatic operation. Interpreta-tion of the analysis and physical experimentation yieldspractical conclusions that can inform preliminary de-sign decisions for a vast range of smart pantograph mastgeometries.

The main limitations of the presented study are re-lated to lack of simulations of real site conditions,namely the dynamic effects of wind, influence of dis-placements of the top of the mast to serviceability ofthe turbine, and the influence of friction in hinges andsupports to the force distribution in the scissor elementsand to the power requirements of the actuator. The re-alization of hinges may be challenging, as they are sup-posed to allow rotations between elements in two scis-sor planes, but also rotations between these two planeswith minimal friction. Finally, an optimal sensor net-work allowing an accurate mapping of wind forces (asper Equation (8) and robust algorithm that govern themast deployment and adaptability should be developedand tested. All these challenges should be addressed inthe future second phase of the project. The validationshould include testing of scaled model in a wind tunneland a large-scale testing on-site.

The presented analysis and the physical experimenta-tion suggest future avenues of research related to full-scale robustness, kinematics and control framework. Inparticular detailed global stability under the wind, real-ization of details, power consumption, and robust con-trol system will be addressed in the future research.

ACKNOWLEDGMENTS

Initial designs for deployable wind turbine masts shownin Figure 1 were developed with funding from the Na-tional Science Foundation under project grant CBET-1036415. The authors would like to thank Ashley Thrall,University of Notre-Dame, USA for her valuableadvice.

The smart mast prototype was built with precioushelp of departmental undergraduate students Sabrina

Siu and Thomas Mbise, graduate student MeghanKrupka, and technician Joseph Vocaturo.

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