bicicleta analisis

COMPLIANT ROAD BICYCLE BRAKE

Brian M. Olsen Larry L. Howell Spencer P. Magleby

[email protected] [email protected] [email protected]

Department of Mechanical Engineering

Brigham Young University

Provo, Utah, USA

Copyright 2010 BYU

1 Introduction

A driving factor in the bicycle component industry isto increase device performance and decrease the over-all weight. These criteria have led to advanced ma-terials and novel designs. One way to achieve theseobjectives is to decrease the number of componentsin the overall design. The purpose of this work isto use the advances in compliant mechanisms theoryto develop a bicycle brake with the potential for lowweight and high performance (i.e. compact designwith a consistent mechanical advantage). This willbe performed by incorporating a library of compliantmechanisms with rigid-body replacement synthesis.

Compliant mechanisms achieve motion or forcetransmission through the deflection of flexible mem-bers [1]. Using compliant mechanism theory to de-sign a bicycle brake that achieves motion throughthe deflection of compliant members has a potentialto decrease the number of parts and lower the overallweight, while maintaining or improving the perfor-mance. Compliant mechanism theory has previouslybeen used to design bicycle components improvingthe performance of a mountain and BMX brake and arear derailleur [2], and a clipless pedal [3]. This chap-ter will incorporate compliant mechanisms to designa novel road bicycle brake.

2 Background

This section provides a review of information relatedto (1) compliant mechanism design methods, and (2)the necessary functionality of brakes.

2.1 Compliant Mechanism Design

Methods

The maturation of the analysis and synthesis ofcompliant mechanisms continues to improve allow-ing compliance to be incorporated into commercialproducts [4]. This advancement of compliant mech-anisms has lead to a development of design method-ologies [512], one being rigid-body replacement syn-thesis, and a development of a reference library forcompliant mechanisms [13].

2.1.1 Rigid-Body Replacement Synthesis

Rigid-body replacement synthesis involves designingor identifying a rigid-body mechanism that accom-plishes the desired function and then converting thedesign into a compliant mechanism [14]. This con-version process can be achieved by two approaches.The first approach is to decompose a complex mech-anism into mechanisms that have a simpler function,and then replacing the respective mechanism with acompliant counterpart. The second approach is to re-place the rigid-body elements with a compliant coun-

1

terpart. Permutations of compliant mechanisms canbe found by using type synthesis.

The rigid-body mechanism in rigid-body replace-ment synthesis can be referred to as the pseudo-rigid-body model. The pseudo-rigid-body model predictsthe deflection path of flexible segments by modelingit with characteristic pivots (i.e. rigid links attachedat pin joints with torsion springs), see Figure 1.

A major challenge associated with rigid-body re-placement synthesis is that while rigid-body mech-anisms kinematics and kinetics can be decoupled,the kinematics and kinetics of compliant mechanismsare highly coupled. One technique to overcome thischallenge is to design a rigid-body mechanism for thegeneral motion of the mechanism, then convert themechanism into a compliant mechanism. This com-pliant counterpart could then be improved by usingoptimization techniques to obtain the desired forcesand motion through finite element analysis (FEA).

2.1.2 Library of Compliant Designs

Previous work establishes a classification scheme forthe purpose of helping engineers find existing compli-ant designs that they can incorporate into their ownapplications [13]. The classification scheme catego-rizes compliant designs by three approaches, with theprimary approach being functionality. This approachwill be used throughout this chapter because thefunctionality classification approach categorizes com-pliant designs into respective classes that work wellwith rigid-body replacement synthesis. The func-tionality approach separates compliant designs intoElements of Mechanisms and Mechanisms and arethen subdivided into subcategories, classes, and sub-classes, according to their respective function.

Olsen et al. [15] have illustrated how this classifi-cation scheme could be used as a basic framework fora library of designs that could be incorporated intothe design process. This is done by using the func-tionality classification approach in conjunction withrigid-body replacement synthesis to design a mecha-nism that has flexible segments.

2.2 Self-Centering Mechanism

The kinematics of a mechanical brake system requirestwo characteristics to achieve a good design: (1) theshoes (pads) should self-center about the rim duringthe actuation process, and (2) the forces should bebalanced on the rim. Brooks et al. [16] presented fourdesign principles (postulates) to accomplish these ob-jectives for a mechanical brake system, and also pro-vided a design procedure that utilize these postulates.This work will focus on postulates one and three,which are:

Postulate 1: A minimum of two degrees of free-dom are required in the brake mechanism, in or-der to exhibit simultaneous centering and bal-anced reaction force characteristics.

Postulate 3: To maintain the braking links ina stable equilibrium off position, at least onepotential energy storage device is required foreach degree of freedom in the mechanism.

3 Rigid-Body Brake Designs

The industry for road bicycle components is a fairlylarge and competitive, where many providers try toproduce a high performance device with minimalweight. This is especially true for brake systems,where high performance is required due to the highloads the brakes undergo while being actuated, whilemaintaining a minimal weight. There are, however,few rigid-body linkage designs that have been estab-lished to achieve this objective, where most designvariables are focused on material selection, accessoryfunctions, and integrated components. Thus, thenovelty of these designs are not contingent on theirkinematic and kinetic functions.The purpose of this research is to present a new

linkage configuration that will inherently use less ma-terial, and remove the need for integrated compo-nents. To begin, an understanding of the existingbrake designs with their advantages and disadvan-tages is requisite, to better understand a benchmarkfor the compliant bike brake. There are primarilyfive rigid-body linkage designs, which will be referred

2 Copyright 2010 BYU

Pseudo Spring

Characteristic Pivot

(a) Pseudo-rigid-body model (b) Small-length flexural pivot

(c) Fixed-pinned flexible beam (d) Cross axis flexure

Figure 1: The (a) pseudo-rigid-body model concept for a (b) small-length flexural pivot, (c) fixed-pinnedflexible beam, and (d) cross-axis flexure

to as: (1) cantilever, (2) single pivot, (3) modifiedsingle pivot, (4) dual pivot, and (5) modified dualpivot. A schematic of these designs along with theiradvantages and disadvantages are shown in Table 1.

3.1 Synthesis of Alternative Configu-

rations

The modified single pivot and modified dual pivotrigid-body brake designs shown in Table 1 functionwith a higher kinematic pair (i.e. cam). These de-signs do not allow a greater number of compliantconfiguration counterparts to be formed by rigid-body replacement synthesis because most compliantelement designs are established for lower kinematicpairs. Thus, by transforming the higher order kine-matic pairs to equivalent combinations of lower orderpairs, more compliant permutations can be found.

Titus et. al. [17] gave a list of transformation lawsfor basic kinematic chains. The fourth law is helpfulin converting existing rigid-body designs into alterna-tive configurations that have a similar function. Thefourth law states that a removal of a pin-connectedbinary link and substitution of a higher pair joint forthe binary link and its 2 lower pair joints will notchange the degrees of freedom. The opposite is alsotrue, where a binary link substituted for a higher pairjoint will not affect the degrees of freedom. This lawis helpful for the modified single pivot and modifieddual pivot brake designs, where their cams can be

replaced with a binary link which will be more ad-vantageous in converting the design into a compliantcounterpart. By utilizing this law, equivalent configu-rations for the modified single and dual pivot designsare shown in Figure 2.

4 Rigid-Body Replacement

Synthesis

In preparation for rigid-body replacement synthesisa screening matrix was performed on the rigid-bodydesigns of Table 1 based upon multiple criteria, in-cluding the designs (1) eligibility to be converted intoa compliant mechanism, (2) target mechanical advan-tage, (3) number of parts, (4) ability to self-center,and (5) angular deflections. The resulting design thatis most eligible for conversion based upon the criteriais the modified dual pivot. As established in section3.1 there are two possible rigid-body configurationsassociated with this concept: the higher-order pairdesign (Cam Design) and the lower-order pair design(Linkage Design).

4.1 Compliant Counterparts

Rigid-body replacement synthesis treats the rigid-body linkage configuration as a pseudo-rigid-bodymodel. That is, the rigid links and pin joints can bereplaced with a compliant element that has similar


Table 1: Road bicycle brake comparison

NAME ADVANTAGES DISADVANTAGES IMAGE

Cantilever

Reduced number ofparts Force balanced Free of debris

Cable housing Two mounts

SinglePivot

Reduced number ofparts Less expensive tofabricate

Rotate about mount Mechanical Advantage

ModifiedSinglePivot

Mechanical advantage High performance

Rotate about mount Number of parts Varying mechanicaladvantage

Dual Pivot Force Balance Less expensive tofabricate

Cable housing Number of parts Number of attachmentpoints

ModifiedDual Pivot

Reduced number ofparts Compact High performance

Force Balanced Lever arm rotation


Input

Input

GroundCam

Output

(a) Modified cam single-pivot schematic

Ground

Cam

Input

Input

Output

(b) Modified cam dual-pivotschematic

Input

Input

Ground

Output

(c) Modified linkage single-pivot schematic

Ground

Input

Input

Output

(d) Modified linkage dual-pivotschematic

Link 1 Link 3

Link 2 Link 4

Revolute

Figure 2: Configurations of ((a)-(b)) higher-order and ((c)-(d)) lower-order kinematic paris


motion. This section describes what type of compli-ant elements would be most beneficial to replace therigid-body elements.

4.1.1 Cam design

In the modified dual-pivot design there are threemain rigid components: a torsion spring, two pinjoints attached to the ground link, and a cam. Thisbrake design has one degree of freedom, which contra-dicts postulate 1 of section 2.2. However, the springin this device plays an important role in that it keepsthe cam in contact with the cam surface and whenone pad makes contact with the rim, the cam is re-moved from the contact surface to achieve its seconddegree of freedom. This behavior makes it a meta-morphic mechanism [18]. It is imperative in rigid-body replacement synthesis that the compliant ele-ment that replaces the pin (attached to the torsionspring) helps maintain this function.Rigid-body replacement synthesis for this concept

(modified dual pivot with a cam) allows the two pinjoints to be replaced by a compliant element. As com-pliance achieves energy storage through deflection, itcan remove the need for the torsional spring. It isalso important to note that the compliant elementsthat replace the pin joints need to have a high off-axis stiffness due to the high loads experienced dur-ing braking. Other requirements are that the elementshould be able to undergo large deflections for com-pliant mechanisms and be compact. By examining alibrary of compliant elements [15] that match thesecriteria, some possible candidates are the cross-axisflexure and the tubular cross-axis flexure [19]. Theresulting compliant replacement possibilities can befound in Table 2.

4.1.2 Linkage design

This mechanism design is similar to the cam designdescribed in the previous section, but it has a bi-nary link that replaces the cam (see Figure 2). Thus,the compliant replacements for the ground pins aresimilar to the cam design, but the binary couplerlink can easily be converted into a compliant equiv-alent. The requirements for this type of compliant

element replacement is that they should be able toundergo large rotations, be compact, and may be re-quired to have energy storage if the ground pins arerigid-link joints. By examining a library for compli-ant elements [15] that fit this criteria, two possiblecandidates for the coupler link are a fixed-fixed andfixed-pinned compliant beam. The resulting compli-ant replacements can be found in Table 2.

A challenge with this rigid-body design, accordingto the first postulate (see section 2.2), the mechanismneeds at least two degrees of freedom. The mecha-nism shown in Figure 2(d) is a four bar mechanismand has one degree of freedom. The second degree offreedom is accomplished through system compliance.For example, a compliant beam can achieve a seconddegree of freedom by entering into another mode ofmotion (i.e. buckling).

4.2 Selection

A preliminary finite element analysis was conductedon the design configurations found in Table 2. Thepurpose of this analysis was to determine which con-figuration provided a sufficient amount of energy stor-age through actuation, while maintaining minimalstresses. It was found that the fully compliant de-signs (i.e. no rigid pin joints), and the configurationswhere the ground link has rigid pin joints and a fixed-fixed coupler link would result in designs that willperform similar to the benchmark. A challenge witha fully compliant brake design is the mounting pin,where one ground pin has a dual role as a rigid pinjoint and also the mounting point. The design thatwill be featured in the rest of this chapter is the link-age design where the ground link has rigid pin jointsand the coupler is a compliant fixed-fixed beam.

5 Compliant Brake Design

The resulting compliant design concept originatedfrom the modified dual-pivot brake (see Table 1).This design was then transformed from a higher-orderkinematic pair to lower-order kinematic pairs (seeFigure 2(d)), which proves to be a better candidatefor rigid-body replacement synthesis. By using type


Table 2: Rigid-body replacement options

Ground LinkCoupler Link

Pin 1 Pin 2

CamDesign

rigid pin joint rigid pin joint cam

tubular cross-axis flexure tubular cross-axis flexure cam

tubular cross-axis flexure cross-axis flexure cam

cross-axis flexure tubular cross-axis flexure cam

cross-axis flexure cross-axis flexure cam

LinkageDesign

rigid pin joint rigid pin joint fixed-fixed beam

tubular cross-axis flexure tubular cross-axis flexure fixed-fixed beam

tubular cross-axis flexure cross-axis flexure fixed-fixed beam

cross-axis flexure tubular cross-axis flexure fixed-fixed beam

cross-axis flexure cross-axis flexure fixed-fixed beam

rigid pin joint rigid pin joint fixed-pinned beam

tubular cross-axis flexure Tubular cross-axis flexure fixed-pinned beam

tubular cross-axis flexure cross-axis flexure fixed-pinned beam

cross-axis flexure tubular cross-axis flexure fixed-pinned beam

cross-axis flexure cross-axis flexure fixed-pinned beam

synthesis, permutations of compliant configurationswere generated. After creating a screening matrix,the compliant mechanisms concept that proved to bethe most advantageous was one where the ground linkhas rigid pin joints and the coupler link is a compliantfixed-fixed beam (first row of Linkage Design in Ta-ble 2). The pseudo-rigid-body model of this conceptis shown in Figure 3.

5.1 Optimization

The next step in the design process was to optimizethe mechanism for mechanical advantage and forcebalance. Two separate optimization problems weresolved, with objectives of maximizing the mechanicaladvantage and the force balance. The brake designis required to fit in a specified envelope, thus the in-put/output and mounting points are constrained toa relative location, so the design variables are theplacement of the second ground (non-mounting) rigidpin joint and the characteristic pivot locations of thecompliant coupler.

The mechanical advantage and force balance equa-

tions were derived using the principle of virtual work.The mechanical advantage derivation did not includethe pseudo torsion springs, because its focus wasto find the kinematic mechanical advantage. Themechanical advantage (MA) for this multi-degree-of-freedom mechanism is described as the ratio of theaverage output forces to the average input forces.

MA =(Fout)average(Fin)average

(1)

By using the principle of virtual work [1] it wasfound that the primary design variable for mechani-cal advantage is the location of the second rigid pinjoint of the ground link, where the location of thecoupler characteristic pivots have a negligible effect.This is helpful because the force balance optimiza-tion routine has one less design variable and can bemore dependent on the geometry and placement ofthe compliant coupler link. The resulting mechanicaladvantage is 1.25 for the optimized link lengths andangles (see Table 3). These dimensions correspond toFigure 4.The next optimization routine was to optimize the


Link 1(Ground Link)

Pseudo Pin(Torsional Spring)

Link 3(Coupler Link)

Link 2

Link 4Pseudo Pin(Torsional Spring)

Rigid Link Pin(Mounting Post)

Rigid Link Pin

OutputOutput

Input

Input

Figure 3: Pseudo rigid-body model of the compliant road bicycle brake concept

Table 3: Optimized bicycle brake values

Pseudo-Rigid-Body Model Compliant MechanismLink Lengths (mm) Link Angles () Link Lengths (mm) Link Angles ()L1 30.245 1 190.000 L1 30.245 1 190.000L2 25.000 2 324.204 L2 28.670 2 326.476

(L2)i 61.936 (2)i 85.000 (L2)i 61.936 (2)i 82.727(L2)o 35.881 (2)o 135.402 (L2)o 34.248 (2)o 127.482L3 43.294 3 161.517 L3 50.934 3 161.517L4 10.000 4 25.814 L4 7.740 4 45.976

(L4)i 66.991 (4)i 140.000 (L4)i 70.807 (4)i 119.606(L4)o 44.886 (4)o 111.316 (L4)o 44.886 (4)o 131.478


L 11

(a) Ground link(segment 1)

(L2) inp

ut

(L2 )

(L2 )

outp

ut

(2)output

(2)input

2

(b) Right side rigid seg-ment (segment 2)

L3

3

(c) Compliant segment(segment 3)

(4)

output

(L4)input(

L 4)

(L4) o

utp

ut

(4)

input

4

(d) Left side rigid segment (segment 4)

Segment 4

Segment 2

Segment 3Segment 1

(e) Brake assembly (back view)

Figure 4: Assembly and dimensions of bicycle brake


force balance, constrained for the given mechanicaladvantage listed above. Force balancing refers to hav-ing the output forces equal,

(Fout)1(Fout)2

= 1 (2)

so the pads will have equal wear when actuated andhave a similar actuation rate. The output forces werefound by using the principle of virtual work. Thedesign variables were only the placement of the flex-ible fixed-fixed beams characteristic pivots and thepseudo torsion springs potential energy.The potential energy equation needed for the prin-

ciple of virtual work for the pseudo torsion springsis

V =1

2K( o)

2 (3)

where V is the potential energy, K is the torsionspring constant for the pseudo springs, and ( o)is the angular deflection. The spring constant for thepseudo torsion springs can be approximated by thefixed-guided beam equations (see Figure 5) [1]. It isnoted that the bicycle brakes flexible beam will notundergo a fixed-guided deflection, but that it will givean approximation for a closed form solution used bythe optimization routine. The spring stiffness for thefixed-guided beam is

K = 2KEI

l(4)

where and K can be approximated as constants,

= 0.8517 (5)

K = 2.65 (6)

E is Youngs modulus, I is the moment of inertia,

I =bh3

12(7)

and l is the length of the flexible segment.

l =L3

(8)

The cross section dimensions of the flexible beam areindicated in Table 4. Titanium and E-glass are used

for the flexible segment and their material propertiesare indicated in Table 5. The resulting optimized linklengths and angles are listed in Table 3, with thesedimensions corresponding to those indicated in Fig-ure 4. The number of flexures listed in Table 4 refersto the number of flexures, of the thickness listed, thatare stacked together like leaf springs. This stacking offlexures allows an increased overall stiffness withoutincreasing stress.

5.2 Analysis

The deformation and stresses were analyzed for theoptimized brake dimensions. The fatigue strength forthe flexible segment was estimated as listed in Table6. It was then determined that e-glass shoudlbe usedfor the compliant mechanism, because of its perfor-mance compared to titanium (see Tables 4 and 6).A commercial finite element analysis software (AN-

SYS) was used to compute the deformation and stressof the compliant mechanism. To simulate a cable ten-sion a vertical displacement was applied to the left-side rigid segment input arm and a vertical force wasapplied to the right-side rigid segment input arm.The applied force was found by determining the re-action force from the displacement and applying theopposite direction force to the applied force, and theniterating this approach until the reaction and appliedconverge (see Appendix 7).To verify that the boundary condition method was

suitable and also that beam elements are accuratefor this type of analysis, three different type of anal-yses were performed: (1) pseudo-rigid-body modelwhere the flexure is approximated as a fixed guidedbeam (see Figure 5), (2) FEA beam element, and (3)FEA shell element. The results are shown in Table7. These results indicate that all methods producesimilar deflections; however, the pseudo-rigid-bodymodels stress is off by a factor of ten. This is mostlikely do to the assumption that the flexure is fixed-guided.The maximum operating deflection (input dis-

placement is 37 mm) and the associated stress forthe mechanism were also analyzed. The stress dis-tribution and deflection of the compliant mechanismis shown in Figure 6. These results predict that


Table 4: Cross sectional geometry

Titanium E-GlassNumber of flexures 10 1Width (mm) 8 8Thickness (mm) 0.508 2.5

Mo

P

(1 )

2l

(1 )

2l

l

lPseudo Torsion

Spring

Pseudo Torsion

Spring

(a) Pseudo-rigid-body model

Mo

P

l

(b) Fixed-guided beam

Figure 5: Fixed-guided flexible beam pseudo-rigid-body model

Table 5: Material properties

Titanium(Ti-5A1-2.5Sn annealed) [1] E-Glass [2]Layer configuration NA w,o,o,wYoungs Modulus (GPa) 114 9.9Tensile Yield Strength (MPa) 779 1,800Ultimate Tensile Strength (MPa) 827 3,400

Table 6: Fatigue strength

Titanium E-GlassNumber of cycles 25x103 25x103

Safety Factor 1 1Fatigue Strength (MPa) 630.981 2,594


Table 7: Analysis comparison of the pseudo-rigid-body model, FEA beam element, and FEA shell elementapproach

Analysis Type Input Displacement (mm) Output Displacement (mm) Stress (MPa)Pseudo-Rigid-Body Model 15.83 12.70 19.32

FEA (Ansys - Beam) 17.23 14.09 182.58FEA (Ansys - Shell) 16.85 14.07 180.33

Note: flexure was e-glass with a cross-section of 8 x 2.5 mm

Figure 7: Force vs. deflection curve comparison

the compliant bicycle brake operates within the de-sired deflection (left side rigid segment and rightside rigid segment displaces 17.91 and 11.99, respec-tively) and prescribed allowable stress (186.57 MPa).

Additional analysis was also performed to comparethe force-deflection curve of different cross-sections tothe benchmark (i.e. modified dual pivot design), seeFigure 7. The results indicate that the compliantdesign has a less constant force than the rigid-bodydesign.

5.3 Discussion

A compliant bicycle brake concept was developedthat has the potential for weight reduction and per-forms similarly to the benchmark (modified dualpivot design). The brake undergoes the desired oper-

ating deflection and the flexible beams stress is belowthe allowable fatigue strength. This analysis was per-formed on two materials: titanium and e-glass. Thee-glass version results in fewer flexures, than the tita-nium version, to perform the same as the benchmark.Thus, different materials could be used for this designconcept as long as it meets the engineers specificationand is aesthetically pleasing.An issue relating to this design is the actuation

rate of the output links, where they undergo an op-erational displacement ratio of 1.34. However, it isnoted the benchmark has a deflection rate ratio of1.2. Thus, it can be seen that the compliant bicyclebrake behaves similar to the benchmark brake.The potential for weight reduction comes from the

removal of material by eliminating the cam and camfollower surface of the benchmark. Also, this conceptremoves the need of four accessory components, thusreducing assembly and further reducing weight. Apreliminary demonstration of the CAD and physicalprototype of this design are shown in Figures 9 and 8.An industrial design concept is illustrated in Figure10.

6 Conclusion

The bicycle component industry is motivated to in-crease performance and decrease the overall weightof devices. This chapter has used compliant mecha-nism theory to integrate compliance into a road bicy-cle brake, and the resulting design has a potential ofreducing the overall weight of the device while main-taining a desired performance.The resulting compliant bicycle brake developed in


(a) von Mises Stress (b) 3D deformation

Figure 6: FEA results from ANSYS for the e-glass flexure

this chapter proved to maintain the benchmark per-formance, and also has the potential of lower weightand reduced assembly by the removal of four acces-sory components.

7 Acknowledgements

The graphics for the brake concept was provided byLarrin Wada, and the prototype was fabricated byNathan Llewellyn.

References

[1] Howell, L. L., 2001. Compliant Mechanisms.Wiley-Interscience.

[2] Mattson, C. A., Howell, L. L., and Magleby,S. P., 2004. Development of commercially vi-able compliant mechanisms using the pseudo-rigid-body model: case studies of parallel mech-

anisms. Journal of Intelligent Material Systemsand Structures, 15(3), pp. 195202.

[3] Look Cycle International, 2010. Keo blade, Aprilhttp://www.lookcycle.com/keoblade/.

[4] Ananthasuresh, G. K., and Kota, S., 1995. De-signing compliant mechanisms. Mechanical En-gineering, 117(11), pp. 9396.

[5] Berglund, M. D., Magleby, S. P., and Howell,L. L., 2000. Design rules for selecting anddesigning compliant mechanisms for rigid-bodyreplacement synthesis. In Proceedings of theASME International Design Engineering Tech-

nical Conferences.

[6] Murphy, M. D., Midha, A., and Howell, L. L.,1996. The topological synthesis of compliantmechanisms. Mechanism and Machine Theory,31(2), pp. 185199.

[7] Frecker, M., Ananthasuresh, G., Nishiwaki, S.,Kikuchi, N., and Kota, S., 1997. Topolog-


(a) Isometric view

(b) Front view (c) Back view

Figure 8: CAD concept of the compliant road bicycle brake


(a) Isometric view (b) Front view

Figure 9: Prototype of the compliant road bicycle brake

ical synthesis of compliant mechanisms usingmulti-criteria optimization. Journal of Mechan-ical Design, Transactions of the ASME, 119,pp. 238245.

[8] Kim, C. J., Kota, S., and Moon, Y., 2006. Aninstant center approach toward the conceptualdesign of compliant mechanisms. Journal ofMechanical Design, Transactions of the ASME,

128(3), pp. 542 550.

[9] Saxena, A., and Ananthasuresh, G. K., 1998.An optimality criteria approach for thetopoloty synthesis of compliant mechanisms. InProceedings of the ASME International Design

Engineering Technical Conferences.

[10] Saxena, A., and Ananthasuresh, G. K., 2000.On an optimal property of compliant topolo-gies. Structural Optimization, 19(1), pp. 3649.

[11] Hopkins, J. B., and Culpepper, M. L., 2010.Synthesis of multi-degree of freedom, parallel

flexure system concepts via freedom and con-straint topology (fact) - part i: Principles. Pre-cision Engineering, 34(2), pp. 259 270.

[12] Hopkins, J. B., and Culpepper, M. L., 2010.Synthesis of multi-degree of freedom, parallelflexure system concepts via freedom and con-straint topology (fact). part ii: Practice. Pre-cision Engineering, 34(2), pp. 271 278.

[13] Olsen, B. M., Hopkins, J. B., Howell, L. L.,Magleby, S. P., and Culpepper, M. L., 2009.A proposed extendable classification scheme forcompliant mechanisms. In Proceedings of theASME International Design Engineering Tech-

nical Conferences.

[14] Howell, L. L., and Midha, A., 1996. Loop-closure theory for the analysis and synthesis ofcompliant mechanisms. Journal of Mechani-cal Design, Transactions of the ASME, 118(1),pp. 121125.


(a) Isometric view

(b) Front view (c) Back view

Figure 10: Concept of the compliant road bicycle brake


[15] Olsen, B. M., Yanal, I., Howell, L. L., and Ma-gleby, S. P., 2010. Utilizing a classificationscheme to facilitate compliant mechanism de-sign. In Proceedings of the ASME InternationalDesign Engineering Technical Conferences.

[16] Brooks, S., Magleby, S. P., and Howel, L. L.,2005. Grasping mechanisms with self-centeringand force-balancing characteristics. In Proceed-ings of the ASME International Design Engi-

neering Technical Conferences.

[17] Titus, J. E., Erdman, A. G., and Riley, D. R.,1989. The role of type synthesis in the design ofmachines. In Proceedings of the NSF Engineer-ing Design Research Conference, pp. 451474.

[18] Dai, J. S., and Jones, J. R., 1999. Mobility inmetamorphic mechanisms of foldable/erectablekinds. Journal of Mechanical Design, Transac-tions of the ASME, 121(3), pp. 375382.

[19] Jensen, B. D., and Howell, L. L., 2002. Themodeling of cross-axis flexural pivots. Mecha-nism and Machine Theory, 37(5), pp. 461476.

A ANSYS BATCH FILE

The following ANSYS batch file can be used to per-form finite element analysis results similar to thoseshown in Figure 6.

Finish/Clear/Begin/filname,BikeBrake,1/prep7!Constantsn=1 !Titanium n=2 and E-Glass =1t=2.5 !Titanium t=2.5 and E-Glass =0.508b=8a=b*n*ti=b*n*(t)**3/12!Material ConstantsE=9.9e3. !Titanium E=144e3 and E-Glass =9.9e3v=0.3

!Set Element TypeET,1,BEAM3!Real ConstantsR,1,a,i,t , , , ,R,2,1e6,1e9,1, , , ,!Material PropertiesMP,EX,1,EMP,PRXY,1,v!Key pointsK,1, 40.464 , 46.891 , 0K,2, 0 , 0 , 0K,3, 23.358 , -15.650 , 0K,4, 26.265 , -50 , 0K,5, 44.164 , -17.322 , 0K,6, -23.863 , 0.131 , 0K,7, -29.786 , -5.252 , 0K,8, -26.270 , -50 , 0!Create linesL,1,2L,2,3L,3,4L,5,6L,6,7L,7,8L,3,6!Create MeshESIZE,,500Type,1REAL,1LMESH,7ESIZE,,5Type,1REAL,2LMESH,1LMESH,2LMESH,3LMESH,4LMESH,5LMESH,6!Non-linear analysisiterat=30steps=3fred=5*DO,i,1,iterat,1Finish/solu


ANTYPE,0NLGEOM,on*do,j,1,steps,1DK,2,Ux,0DK,2,Uy,0DK,7,Ux,0DK,7,Uy,0DK,5,Uy,8*j/stepsf,502,fy,-fredLSWRITE,j*enddoLSSOLVE,1,steps,1finish/POST1set,last*GET,reactfy,NODE,517,RF,fy*SET,fred,reactfyfinish*endDo/POST1PLDISP,1ETABLE,MSTRESS,NMISC,1PLETAB,MSTRESS,NOAV


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