Cam versus Linkage struct a simple scale model of cardboard or aluminum sheet stock to check The cam is in wide use and in many cases offers a very satisfactory the linkage for bad angularity between links,exeessive torque ratio,and solution.In many instances,however,the cam design limits the perform- poesible interferences. ance of the machine.Often,in such eireumstances,a suitable linkage removes the cam-impoeed diffieulties.Because of the difficulty of synthe- Velocity Determination siging a linkage to achieve a specific motion it is common practice to Consider the trajectory shown in figure 16.The point moving along eliminate the linkage from the design in favor of the cam despite certain the trajeetory traverses a distance ab measured along the path in an interval limitations.It is hoped that these charts will facilitate the wider use of required for the drive crank to move through 5.If the drive erank is linkages in such problems. rotating at a uniform angular speed the average velocity of the point during The cam has certain distinctive advantages.It is very flexible.It this travel is the length ab divided by the time the drive crank requires to can be easily designed to give a wide variety of motions.It can be made move through5°. small and compaet.It is,however,subjected to very high stresses at the (V)-(ab)w points of eontaet.The cam follower must be constrained to follow the 5 cam contour either by a spring which raises the stress level on the cam where Va -average velocity of point moving along trajectory from or by a.grooved slot in which the bncklash causes trouble at high speeds point a to point b (inches per second). of operation.In order to limit the dynamie forces at high speeds to allow- ab length between a and b measured along trajectory (inches). able levels the degree of accuracy required in the finishing of the cam w-angular speed of drive crank (degrees per second). contour is beyond the abilities of most shops and in any event results in Aceeleration Determination an extremely expensive operation.The net result is that the top speeds The acceleration of a point moving in space is defined by the following of many machines are set by the limitations of eams.Inereasing the speed relationships. results in excessive machine vibrations and rapid eam wear.Proper cam design and careful machining ean raise such limitations.(See referenee 4.) Linkages very often offer distinct advantages over eams.As the motion is determined by the relative length of the links,small percentage d variations in these lengths do not radienlly influence the reaulting motion. Furthermore,the machining operations are simple and can be performed (-。-bcbw 25 with preeision in any shop.Location and machining of the bearings at the link pivots is standard procedure.Link length tolerances of the order Thus,an approximation of the acoeleration atis found by evaluating of 40.002 inch are easily obtainable and usually adequate.In cam manu- the vector differenee (be -ab)and multiplying by the factor (/25). facture required tolerances for high-speed operation are of the order of 0.0002 inch.In addition the stress levels at the pivots of a linkage are more favorable than they are at the eam surface. Balancing of Linkages If a linkage is to be operated at significant speeds careful attention must be paid to the dynamie forces produced.It is important to keep the mass of the moving links as small as poesible.Aluminum or magnesium alloys with a low-weight high-stiffness eross-seetion design reault in link members with low inertia forces.To prevent the transmission of large ocilating forees to the linkage supports,inertia forees should be balanced. The subject of balancing linkages is covered in reference 1. Use of Models in Design Work Fig.16 The charts give motion eharaeteristies of many linkages and therefore lead direetly to theeetion of the basic link ratios.It is advisnble tocon [i]~ " (xix) Cam versus Linkage The cam is in wide solution. In many instances, however, the cam design limits the perform￾ance of the machine. Often, in such circumstances, a suitable linkage removes the cam-imposed difficulties. Because of the sizing a linkage to achieve a eliminate the linkage from the design in favor of the cam despite certain limitations. It is linkages . in such. problems. The cam has certain distinctive can be easily designed to give a wide variety of motions. small and compact. , however, subjected to very high stresses at the points of contact. The cam contour either by a spring which or by a,grooved slot in which the backlash causes trouble at high of operation. In order to limit the able levels the degree of contour is beyond the abilities of most shops and in any event results in an extremely expensive operation. of many machines are set by the limitations of results in excessive design and careful machining can raise such limitations. Linkages very often offer distinct motion is determined by the relative length of the , small percentage variations in these lengths do not radically influence the Furthermore, the machining With precision in any shop. the link pivots is standard of ::i::O.OO2 inch are easily facture required tolerances for high-speed operation are of the ::i::O.OOO2 inch. In addition more favorable than they are at the cam Balancing of Linkages Ifa must be paid to the dynamic keep the mass of the moving links as small as possible. . alloys with a low-weight members with low inertia oscillating forces to the linkage supports, inertia forces should be balanced. The subject of balancing struct a simple scale the linkage for bad angularity , excessive ' torque ratio, and possible interferences. II! Velocity Determination . Consider the trajectory shown in figure the trajectory traverses a distanceab measured along the path in an interval required for the drive crank to If the drive crank rotating at a uniform angular speed the average velocity this travel is the length ab divided by the time the drive crank requires to move through 50 where (V"b) (ab)"" V"b = average velocity of point point to point (inches per second). ab = length between and measured along trajectory "" = angular speed of drive crank Acceleration Determination The acceleration of a point moving in space relationships. = lim . = ~t ~t--O dV acc. '= - dt = hm ~t--O Vb" - V"b (be - ~t ~t 25 . Thus, an approximation of the acceleration at is found by evaluating the vector 2/25). Use of Models in Design Work Ti!e charts give motion characteristics of many linkages aIid therefore lead directly to the selection of the basic link ratios. It Fig. 16