Desig Optimizatio of the Parameters of Cyclig Equipmet Based o Ergoomics Shu Qiao 1*, Jiagfeg Lua, Da Dig 1 Liaoig Shihua Uiversity, Liaoig, Fushu,113001,Chia Physical fitess testig ceterliaoig shihua uiversity *Correspodig author: Email:64904101@qq.com Abstract - The structure of cyclig equipmet is aalyzed based o Ergoomics i this paper. The cyclig equipmet model is researched ad simplified. After buildig a mathematical model, kiematical simulatio is carried out by Adams modelig ad the dimesios of each part of the cyclig equipmet is optimized by meas of Adams parameter desig accordig to Ergoomics. The ureasoable desig of cyclig equipmet is avoided, ad the researchers propose a affective aalysis ad assessmet method for the alterative desig scheme. Keywords - Cyclig equipmet; Adams; Optimizatio; Ergoomics. I. INTRODUCTION With the improvemet of people s livelihood, fitess idustry ejoys rapid developmet, so stricter requiremet is proposed for the iovatio ad R&D of fitess equipmet. The researchers provide reasoable parameters accordig to Ergoomics, ad simulate it by meas of the theories of kiematics of mechaism, thus optimizig the parameters of the cyclig equipmet, which ca achieve the highest desig efficiecy. Adams is virtual prototype aalysis software developed by America MDI Corporate. It has bee used by hudreds of mai maufacturers i all walks of life all over the world. With this software, users ca coveietly carry out static, kiematic ad kietic aalysis o virtual mechaical system, so as to icrease the desig quality ad shorte the desig cycle. Therefore, this paper obtais the reasoable parameters of the cyclig equipmet by buildig ad simplifyig cyclig equipmet model, ad the it realizes the simulatio ad optimizatio of the simplified cyclig equipmet mechaism via Adams software. The results show that the speed statioarity of the optimized cyclig equipmet is improved withi its operatig stroke, which improves the comfort; the visualizatio ad optimizatio of the mechaism desig is uified by meas of optimizatio desig ad Adams motio simulatio techique. II. DESIGN OF CYCLING EQUIPMENT A. Desig of Cyclig Equipmet Dimesios Based o Ergoomic Priciples With cyclig equipmet, people ca sit o the seat with the hads holdig the hadles, the feet pedalig o the pedals ad the body kept straight ad upright; bedig ad stretchig the arms ad repeatedly ad movig the pedals ca achieve the goal of exercise. This fitess equipmet ca stregthe the muscle stregth of the upper ad lower limbs ad chest muscle, trai waist ad abdomial muscles, ad ehace the fuctios of digestive system ad heart. The specific operatio method is as follow: a perso sits o the seat, pulls the hadles with both hads ad pedals o the pedals with both feet to do back-ad-forth movemet. The basic desig requiremet of its movemet fuctio iclude: (1) the structure dimesios of the cyclig equipmet comply with the huma dimesios of the exercisers; () the reasoable structural form ad structure parameters are desiged to esure the comfortable sports iertia of the cyclig equipmet; (3) the movemet load of the cyclig equipmet complies with mechaics priciples; (4) beautiful appearace complies with the desig requiremet such as athletic psychology etc.[1] The 3-dimesioal model of the cyclig equipmet is as show i Fig.1. Fig.1 Diagram of the 3-dimesioal model of cyclig equipmet. To cater to the fitess demad of most people, the author refers to the stadard released i 1998[] to referece the huma dimesios ad activity space uder sittig positios; the 95th percetiles of male at the age group of 18-66 ad the 5th percetiles of female at the age group of 18-55 are selected as basis for the upper ad lower limit of the dimesios. The spatial positio of the hadles of the cyclig equipmet should be set withi the fuctioal dimesio rage of the exercisers upper limbs. The distace betwee ma ad the hadles should ot be DOI 10.5013/IJSSST.a.17.36.1 1.1 ISSN: 1473-804x olie, 1473-8031 prit
less tha the miimum dimesio of the 95th percetiles of male forearm fuctio ad ot larger tha the maximum dimesio of the 5th percetiles of female forearm fuctio. As the exercises are sittig o the cyclig equipmet, the refereced data are those related to huma dimesios ad activity space uder sittig positios i the atioal stadard. B. Simplify ad Solvig the Model L cos L cos L cos L 0 1 1 3 3 0 L si L si L si 0 1 1 3 3 () (3) The aforesaid equatio ca be simplified to a equatio oly icludes 1 ad 3 by elimiatig, Accordig to the diagram of the 3-dimesioal model, the cyclig equipmet maily cosists of base, seat ad its coectors, hadles ad their coectors etc. The compoets of the cyclig equipmet form a cotra-quadrilateral mechaism, with the base as the rack, the hadles as the drivig levers ad the seat simplified as a follower lever, as show i Fig.. L0 3 ca be solved if 1 is give. Accordig to the above-metioed equatio: si L si L si / L 3 3 1 1 Substitute it ad cos 1si to t1 3si3 1si1 L L t t L cos L cos L L 1 1 3 1 1 3 3 0 L3 (4) (5) L L3 θ3 For kiematic model, the codes ca be coded i Matlab to verify the correctess of the model, as show i Fig.3. L1 θ1 θ Fig. Diagram of the simplified cyclig equipmet. A rectagular coordiate system for the etire mechaism is built, with the hige betwee the base ad the hadles as the origi, positive directio of x axle directig the hige betwee the base ad the seat. The coordiates of each vertex of the lik mechaism are idicated by iitial agle 1 passig the hadles. Poit A, x coordiate 0, y coordiate 0 L Poit D, x coordiate 0, y coordiate 0 L Poit B, x coordiate 1cos 1, y coordiate L1si1 L L cos Poit C, x coordiate 0 3 3, y coordiate L3si 3. i 1 i i 3 L e L e L L e 1 0 3 The real part ad imagiary part ca be differetiated from the above equatio to obtai the follows: Fig.3 The simulatio result of the simplified four-bar model i Matlab. III. ADAMS MODELING AND PARAMETERIZED SIMULATION A. Cyclig Equipmet Modelig i Adams To facilitate parametric desig of cyclig equipmet i Adams, the simplified model of cyclig equipmet eeds to be completed i Adams. (1) Parametric desig process is the process of usig desig variables; the parameter values are replaced by the desig variables, ad the values of desig parameters are chaged by revisig the values of the desig variables [3]. DOI 10.5013/IJSSST.a.17.36.1 1. ISSN: 1473-804x olie, 1473-8031 prit
A series of poits are built, as show i Table 1; ad the poits are coected by the coectig rod commad i toolbox, the the parts ad compoets of the cyclig equipmet is formed by the combied operatio of the two coectig rods. Revolutio joits are added at the rotatig positio after modelig for the parts ad compoets; the directio of the revolutio joits ca be the default Nomal To Grid. TABLE 1 INITIAL COORDINATES OF THE KEY POINTS No. of the parametric poits x coordiate y coordiate Poit1 0 0 Poit 0 96 Poit3 48 0 Poit4 60.8 48 Poit5 3 40 Poit6-5 160 Poit7 90 67. Poit8 3 48 Poit9 35 35 Poit10 18 71 Fig.4 shows the modelig of the simplified two-dimesioal model of the cyclig equipmet i Z Adams. FB is the hadle, 1 lab l1 ; BC is the Z coectig rod, lbc l ; DCG is the seat, Z3 lcd l3 ; EDA is the rack, Z4 lad l4. mi( or / max)g = G(d,d 1...,d) (6) (d,d f1 1...,d) 0 f(d,d 1...,d) 0 s. t. f(d,d 1...,d) 0 (5) a1 d1 b1, a d b,, a d b I this paper, a objective fuctio should be built after makig the rod legth as the desig variable. The cyclig equipmet eeds good drive characteristics durig operatig stroke, with its miimum drivig agle 40-50. I this model, the agle betwee coectig rod AB ad BC as well as the agle betwee coectig rod BC ad CD are measured by way of measure-agle, ad are judged by IF judgmet statemet. Whe the agle is larger tha 180, Temp1=180- ABC, Temp=180- BCD ; accordig to iteratioal stadard, the stretchig rage of the upper limbs uder sittig positio is 71-89mm, d 89 so FG. The four bar mechaism must meet the coditios of a closed plae four bar mechaism, so there is the costrait coditio: g1 ABC 40 g BCD 40 3 1 3 4 0 4 1 3 4 0 5 1 4 3 0 g6 d FG 89 (7) (8) (9) (10) (11) (1) Fig.4 Simplified two-dimesioal model of the cyclig equipmet i Adams. B. Buildig Optimized Mathematical Model Optimal desig is carried out o the basis of desig variable parameterizatio, which optimizes the object desig while meetig costrait coditios ad the value rage of the variables; i.e. Meawhile, the mea value of the cyclig equipmet s drivig agle i operatig stroke shall be as large as possible, so as to esure better drivig performace ad less strict requiremet o materials uder other similar coditios. The miimum mea values of ABC ad BCD durig the etire simulatio process should be selected as the optimizatio object. However, parameter optimizatio simulatio of Adams oly allows sigle object optimizatio, while the four bar mechaism desig is a optimizatio problem with multiple variables ad multiple objects, so the author eeds to covert the multiple objects ito a optimizatio problem of sigle object; i.e., DOI 10.5013/IJSSST.a.17.36.1 1.3 ISSN: 1473-804x olie, 1473-8031 prit
max F(x) k max F k max F 1 1 (15) k1 ad k are the weight values of sigle object optimizatio i multiple object optimizatio. Selectio of the weight values ca be chaged accordig to desig eed; ad they are simplified to be 1 i this paper. The uecessary details are ot repeated here. 3.3 Parameter Optimizatio Simulatio of Cyclig Equipmet i Adams After buildig desig variables, costrait coditios ad objective fuctio, the parameters are alculated ad optimized based o oe workig cycle i Simulate-Desig Evaluatio Tools. The drivig agles betwee AB ad BC as well as that betwee BC ad CD uder 10 statuses are as show i Fig.5 ad Fig.6 respectively. Fig.5 Chage of the drivig agles betwee AB ad BC uder differet parameters. Fig.6 Chage of the drivig agles betwee BC ad CD uder differet parameters. Accordig to the two diagrams, the mea values of the two drivig agles both icrease i each iteratio ad fially reach the optimal solutio. The chagig curve of the sum of the two drivig agles (the objective fuctio) is as show i Fig.7. The chagig tedecy of key poit C is as show i Table. Fig.7 Chagig curve of the objective fuctio. DOI 10.5013/IJSSST.a.17.36.1 1.4 ISSN: 1473-804x olie, 1473-8031 prit
Accordig to Fig.7, the drivig agle icreases obviously i the first three iteratios, the the objective fuctio chages ot so drastically, ad the differece betwee the iitial value ad optimal solutio is ot large. It s complicated to list all the coordiates affectig the rod legth, so the author takes the chage of the coordiates of C poit i each iteratio for referece. I Table, the x coordiate of C poit fluctuates i early iteratio ad the coverges quickly, while its y coordiate chages slowly, which proves that cyclig equipmet desig based o Ergoomics ad optimal desig are cosistet to some extet. TABLE CHANGING TENDENCY OF THE OBJECTIVE FUNCTION AND THE CHANGE OF THE X AND Y COORDINATES CORRESPONDING TO PARAMETERIZED POINT 4. Iteratio umber Objective fuctio value x value of C poit y value of C poit 1 160.0 58.78 44.987 163.81 63.148 43.61 3 166.5 6.035 43.70 4 166.6 6.70 43.00 5 166.69 61.66 43.00 6 166.71 61.34 43.49 7 166.74 60.561 43.703 8 166.75 59.93 43.789 9 166.75 60.136 43.679 10 166.76 60.136 43.679 Natioal Defese Idustry Press, 006. [4] Zheg J R. ADAMS- Etry ad improvemet of prototypig techology [M]. Beijig: Chia Machie Press, 00. [5] Li J, Xig J W. Tutorial Examples of ADAMS [M] Beijig: Beijig Istitute of Techology Press, 00. [6] Liu W X. Mechaical optimizatio desig [M]. Beijig: Tsighua Uiversity Press,1994. [7] Che N C, Huag J L. Liear optimize algorithm for motio sythesis of plaar four-bar likage [J]. Machiery Desig & Maufacture, 007.8:1-. [8] Liag Y J. Research o optimizatio desig for four-bar likage flyig shear [D]. Chagsha:Hua Uiversity,009. [9] Ji X Z, Wag Y X. Trasmissio agle-orieted multi-variable optimizatio desig of slider-crak mechaisms [J].Joural of Shaghai Jiao Tog Uiversity,007, (41)4:561-564. [10] Yag X, Sog J. Structural calculatio ad optimizatio of four-bar likage pumpig uit trasmissio mechaism [J].Joural of Mechaical & Electrical Egieerig, 013,(30): 15-155. [11] Yu S S, He L. Optimal desig of pressig machie s workig mechaism based o software [J].Machie Desig, 013,30():4-7. [1] Fu Z H. The optimizatio desig of crak sildig block mechaism at work flow trasmissio agle [J].Joural of Zhuzhou Istitute of Techology,1997,11():58-61. [13] Guo H L, Zhag L X. Use of the maximum of the miimum trasmissio agle i the optimizatio desig of crak ad slide block mechaisms [J]. Agricultural Mechaizatio Research,004,7(3):195-197. IV. CONCLUSION This paper completes the three-dimesioal modelig for cyclig equipmet by referecig atioal stadard based o Ergoomics, ad simplifies it to a two-dimesioal oe to build a mathematical model ad verifies a reverse four bar mechaism i Matlab. Meawhile, the desig variables of the cyclig equipmet are successfully parameterized i Adams, ad the kiematic parameters of the cyclig equipmet are optimized i lie with the optimizatio priciple ad the referece rage of the atioal stadard. The optimizatio results show that the method proposed i this paper is a fast ad effective method for desigig ad aalyzig cyclig equipmet; it cosiders Ergoomics ad sigificatly reduces the rehadlig i traditioal desig, thus icreasig the R&D cycle ad quality of the products. This method ca be used as a referece method for desigig ad developig cyclig equipmet i future. REFERENCES [1] Zhao C H, Zhag B, Zhag S J. Desig ad imitatio of the ridded-body-buildig machie based o the ergoomics [J]. Mechaical Maagemet ad Developmet, 010.5(1):4-7. [] Wu Z Z, Luo S G. Course desig maual of mechaical desig [M]. Beijig: Higher Educatio Press, 006. [3] Li Z G. Detailed etry ad examples of ADAMS [M]. Beijig: DOI 10.5013/IJSSST.a.17.36.1 1.5 ISSN: 1473-804x olie, 1473-8031 prit