Although refe rred to as a static margi n, the cal culation involves aspect s of mechani cal dyna mics a s well  as stati cs. Of particul ar interest is the imminent or i nitial motion of a machine , and in som e cases the   followin g continuou s motio n. One exam ple is a depl oyable su ch as a sol ar array being rele ased from a  launch lock a nd then moving to its final positio n; another is a sca nning me chanism co ming to  a stop and   then reve rsing dire ction. 

For static m argins, the resi sting loa ds do n ot include velo city-depe ndent lo ads from rate co ntrolle rs.  Coulomb fri ction from b earings, a hyst eresis damp er, or b etween a pa ddle and ho using in a viscou s  dampe r, wo uld be in cluded, howeve r. The obj ect is to determin e if there is sufficie nt driv ing force to  ensure that th e mech anism will start and then not sta ll at any point in its oper ational path or cycle. 

The calculation of force and torq ue ma rgins i s relativ ely strai ghtforward for a simple me chanism such as a  spring-load ed hing e. Howe ver, for complex mechani sms employin g gear trains, linkage s, or jackscrews,  the basi c arithmetic p rocess needs special ad aptatio n. For examp le, the drive actuato r can be se parated   from the driven mem bers by multiple g ear m eshes having sources of fri ction drag at vario us points. T he  probl em be comes mo re co mplex if the g ear train in cludes a cra nk or jackscre w to convert rota ry motion to  linear m otion, which lead s to the que stion as to wh ether to cal culate a force margin or a torqu e margi n. 

The metho d descri bed h erein refere nces drive fo rces and resisting forces, an d moment s, as eq uivalent   force s and m oments at a singl e sel ected point in th e mech anism. This i s done by multiplying each fo rce  or mo ment b y the ratio of  its displa cement to the displacement  at that sel ected coordinate point. Th e  displacement  ratio s time s their respective force s or moments,  from  the va rious points of the  mech anism,  are then  sum med to  colle ct them a s equivalent forc es and mom ents at the selected commo n point. As an   example of the cal culation of margi ns for a co mple x mecha nism, the method will be ap plied to a motor  driving a worm gear, in tu rn drivin g a crank and pi ston throug h a spu r gear. Then the fo rmula will b e  stated in ge neral term s. 

The pr ocedure w ill be developed us ing s mall displa cements  and mechanic al work. The dis cussion w ill  include the relation ship of  this app roach to the method of virtual  displa cements and virtu al work. It wil l  also be shown that fo rce and to rque m argins can be calculated  as ene rgy margins, po wer margin s, or  virtual wo rk margi ns, an d that these ma rgins have a simple relatio nship to mechani cal efficie ncy. 

DEFINITIO N OF FOR CE AND TO RQUE MARGI N 

Force an d Torque M argins were first def ined in a US AF “Specifi cation for Movin g Mech anical Assem blies  for Space Ve hicles…” (MMA Specifica tion, Ref. 1,  1975 ), and t wice revi sed (Ref. 2, 197 8 and Ref. 3,  1988). The basi c definition is used by NASA in a similar form (G EVS, Ref. 4), and in recent years has  been generally adopted  by the ae rospace industry a nd incorporated into company de sign specifi cation s.  Static force margi ns requi red for me chanism s range from 100 percent (Refs. 1 to  3) to 200 percent (Ref.   4). The se are equivalent to safety factors of 2 to 1  and 3 to 1 resp ectively. In some cases, weig ht or  power restri ctions o r a man ufacturer' s past pra ctice has led to the u se of margin s less tha n 100 percent. 

From Refere nce 1, stati c force margin a nd static torque margin ex pressed a s a percenta ge, a re define d  as follows : 

1001Force ResistingForce Drive  Margin Force Static  ⋅   − =                 (1) 

1001Torque ResistingTorque Drive  Margin Torque Static ⋅   − =              (2) 

In Refe rence 3 (198 8), a  change was made to  the f ormula, in th at the force  required fo r acceleration i s  subtracte d from the drive  force. Th is will be  discussed late r. To minimi ze repetition, in t he follo wing  discu ssions the use of the term force m argin will in clude its count erpart, torque  margin, an d vice versa.  108