Mechanisms A Brief Introduction October, 2012

Transcription

1 Mehnisms A Brief Introution Otoer, 2012 A mehnism trnsfers motion n fore from soure to n output. Mehnisms inlue ger trins, liner to rotry onverters, lokworks n more. Mehnisms re everywhere you look from the rive trin of your r to the le srew in your CD plyer. It is likely tht you will use mehnism in your root. A linkge is simple mehnism ontining rigi rs (the links) onnete through pin n prismti (liner) joints. Linkges re simple in struture ut powerful in funtion, proviing elegnt solutions to motion ontrol prolems. For exmple, here re two versions of the slier rnk, ommon linkge,. Imges re tken from tht ontins goo tutorilsout si mehnisms tht you shoul explore. At the right is 4-r linkge tht hs three moving links n one groun link. By vrying the lengths of the moving links n the lotion of nhor joints on the groun link, surprising rnge of tip motion n e proue. You my en up using linkge in your root, perhps the rotry-toliner slier rnk or 4-r. It is likely you will esign or speify linkges in your future reer s professionl mehnil engineer. In ME3222 Design n Mnufturing II you will lern how to esign mehnisms, inluing linkges n will use nlysis softwre to synthesize linkge to proue esire output motion. In this tivity you will uil three si linkges with simple mterils. The onstrution methos, preision n utility of wht you uil will not e memorle, ut you shoul wlk wy with new ppreition for mehnisms n mny ies for how to use linkges in your mhines, inluing your root. Deliverles: Before the l, uil n run ll 3 mehnisms. Along with onstruting n mesuring the mehnisms, there re some homework prolems whih shoul e omplete. Some of the homework questions my e iffiult, ut mke goo fith effort even through you will not e gre on whether the eqution is orret n your erivtions will only e looke t y your tem memers. Bring the mehnisms, ruler, omplete homework prolem n lultor with you to l. Supplies you nee: One sheet of link utouts, 12 srew posts for the joints, offie tpe to join links n nhor groun links. (ME2011 stuents will get the sheet n the fsteners in leture.) Tools you nee: sissors n ruler with millimeter sle. Mehnisms Pge 1 of 5

2 The oxe setions lele L Exerise will e one in l with results entere on supplie worksheet. The questions lele Homework re wht you shoul o in vne to prepre for the l, ut will not e turne in. CONSTRUCTION TECHNIQUE The mehnisms work resonly well if you re reful in your onstrution methos. Cut out the link memers. No nee to e reful in the outline uts. Use hole punh to mke the holes, trying to ple holes extly t the mrke lotions. A penil n e use to mke the hole, ut the mehnism won t run s smoothly. Use the srew posts to onnet links. Before inserting post, fltten ny fringes on the hole ege with your fingers. This will reue joint frition. Pln the ssemly orer so tht links n rotte ll the wy. When rey to operte, lightly tpe the groun link to the tle. You my wnt to fol longer links into U-shpe strut to mke stiffer em. SLIDER CRANK The slier-rnk is si rotry to liner mehnism. It is hny for generting reiproting motion euse the motor oes not hve to reverse iretion. A rtoon of slier rnk is on the front pge of this oument n n strte slier-rnk is shown elow. Link, the rnk, trvels roun in irle through ngle thet. Link, the slier is onstrine y erings to trvel long the otte line. x Homework Question #1: Using your high shool trigonometry, write the eqution, x = f(thet) for the isplement x of the tip of link s funtion of rnk ngle thet. Let x = 0 for when thet = 0 with positive x going from right to left s shown in the piture ove. Leve link lengths n s vriles in the eqution. You might wnt to look up the lw of sines n the lw of osines to help you in eriving the eqution. Homework Question #2: Write seon eqution where the link lengths re reple with the lengths in mm of the slier rnk you will uil, = 40 mm, = 80 mm. Homework Question #3 (optionl): Imgine pushing ginst link with fore F in the iretion shown y the rrow mrke x in the figure. Now imgine tht there is motor riving link n tht the motor is prouing torque T ting in the lokwise iretion tht results in fore through link tht perfetly ounterts fore F. In other wors, the motor is ting through the slier rnk linkge to resist your pushing fore so tht link oes not move. You n see tht the mgnitue of torque T to lne your pushing fore F will epen on ngle thet. Your tsk is to write the eqution T = f(thet, F) for the torque t lnes pushing fore F with the linkge t ngle thet. LINKAGE #1: Slier rnk Construt the slier rnk mehnism shown elow whih hs four links n three joints. The link proportions re = 2*. Anhor the groun link g to the tle. Form U-shpe hnnel with n inex r to use s guie so tht link is onstrine to trvel in stright line. Tpe the hnnel to the tle. Go k n re the onstrution tehniques if the system oes not run smoothly. Mehnisms Pge 2 of 5

3 g inex r hnnel Run the rnk (link ) y hn (normlly the rnk woul e nhore to the motor shft) n mire your work. LAB EXERCISE: Set your onstrute linkge rive rnk to ngles shown in the tle on the work sheet. Strt with thet = 0 n mrk the x = 0 position of the tip of link on the inex r guie. Then move the rnk to the next ngle n mrk the lotion of the tip. After ll ngles re mrke, use the mm sle of ruler to mesure the istne etween eh mrk n the x = 0 mrk. Reor your t on the worksheet tle. Explin ny ifferenes etween the theoretil n mesure positions. (Wrning: Do not just your mesurements to fit the theory s tht woul e sientifi n engineering fru.) In your slier rnk, the enter of rottion of the rnk is in line with the line of tion of the piston. Is it possile to hve slier rnk where the rnk rottes out point off the piston line? Try it. The piston requires liner ering, in this se the inex r guie, to onstrin the motion of link to stright line. Cn you nme n esy to mke or esy to purhse liner motion evies? For exmple, rwer slie is liner motion evie. Work with your group to ome up with t lest 10 liner motion evies. FOUR-BAR LINKAGES A 4-r linkge hs four links n four joints. One of the links is groune n two of the joints re fixe joints whih mens wht you tully see moving re three links. A generi 4-r is shown elow Link is the river rnk n is tthe to the motor. Link is the oupler n link is the output rnk. The tip of link tres the esire output. The fourth link is the groun link whih oes not move n is represente y the istne etween the two groun joints. By hnging the lengths of,, n the istne etween the groun joints, n infinite set of motions for the riven tip n e hieve. A ourse in kinemtis will teh you how to esign 4-rs to hieve Mehnisms Pge 3 of 5

4 given tre funtion. In this tivity, you will uil one 4-r tht tres n pproximte stright line n nother tht ts like n inset leg. One vntge of oing stright line motion with 4- r rther thn slier-rnk is tht the 4-r hs ll rotry n no sliing joints. LINKAGE #2: Stright line motion with 4-r This is remrkle 4-r linkge where the tip of trer r follows stright line pth over muh of the urve s rnk rottes For stright line motion, the link lengths re in the proportions = 2x, = 10x, = 5x, = 4x n the joint etween links n is lote t the mipoint of link. Confirm tht the link lengths on your ut out sheet re in these proportions. Construt this 4-r. Before ssemling link, ut smll hole, out the size of mrker tip t the ple mrke output. LAB EXERCISE: Anhor groun link to the tle n tpe piee of pper uner trer link. Operte y rotting link whih woul normlly e tthe to motor. Every few egrees mke pen mrk t the output of link s link rottes 360 egrees. Connet the ots Or, you might e le to let the link rg mrker ross the pper to mke ontinuous line. You shoul see tht goo prt of the tre pproximtes stright line. Mesurement: With ruler, rw est-fit stright line through the tre over the prt where the tre is losest to eing stright. Mrk where the tul tre evites from the stright line y more thn 5 mm n mrk these limits. Mesure in mm the length of the stright line tre etween those two limits n enter on the worksheet. Whih person in your group ws le to get the strightest line n why? Chllenge: Come up with six root ies for whih this mehnism woul e useful. Mehnisms Pge 4 of 5

5 LINKAGE #3: Inset leg (Apte from the ook Mehnil Devies y B. Rorugh) Here is n interesting mehnism tht lets your rotry motor rive leg in somewht of wlking motion. Link is the input rnk tht is onnete to ger motor. The inset foot is t the tip of link. Link is the groun link whih is the root frme. root floor For this 4-r, the proportions re = 2x = 5x, = 10.5x, n the joint etween link n link is 5.5x wy from the groun pivot on link. The horizontl istne etween the two groun pivots is 5.0x, n vertil istne etween the two pivots is 3.5x. Buil the mehnism. Tpe link to the ege of noteook t pproximtely the ngle shown in the rwing where the noteook represents the root frme. Hol the noteook so tht leg ngles stright own. Operte the rnk n mire your inset. One key feture of this mehnism is tht it onverts ontinuous rottion of motor to reiproting motion of leg. Chllenge: Do you think tht pltform with 4 of these legs ple strtegilly oul e one wy to implement rooti wlking mhine? LAB EXERCISE: Run your inset leg in l. Chllenge: Come up with six root ies for whih this mehnism woul e useful n shre those ies with your group. Mehnisms Pge 5 of 5