Force and Torque Margins for C omplex Mechanical Systems 

Robert W. Po stma* 

Abstract 

Force a nd to rque margin s are comm only use d within the a erospace community to dete rmine if the  actuato r for a mechani sm has sufficient force or  torque to ensure successful ope ration. Typical   mech anism functio ns include de ployin g an anten na, rele asing a launch restrai nt, rotating a  sola r array,  controlling an antenn a poi nting me chanism, ope rating a valve, or relea sing an interface co nnector. Th e  definition of force margin relate s to the ratio bet ween the drivin g force s and the resi sting  loads. For   example, if the driving force is twic e the  resisting loa d, the force margi n is 100  percent. The  calculation o f  force and to rque ma rgins is rel atively straightforwa rd for a simpl e mech anism such as a sp ring-loaded  hinge. Howe ver, for com plex mechani sms employi ng gea r train s, linka ges, and ja ckscre ws, the b asic  arithmeti cal process be comes mo re complex. 

The metho d descri bed h erein refere nces drive fo rces, and resi sting force s and mome nts, as equivale nt  force s and m oments at a selected p oint in the mec hanism. Thi s is don e by multiplying e ach fo rce or  moment by t he ratio of its di splacement to the di splacement at  that sele cted coordinate point. The se  equivalent force s from the variou s point s of the mechani sm are t hen su mmed  at the select ed com mon  point, kee ping driving forces sepa rate f rom resi sting force s, for u se in the basi c force a nd torque ma rgin  formula s. It is sho wn that force and to rque margin s can be calcul ated as en ergy margin s, po wer m argins,  or virtual work margin s, an d that these margi ns have a simple rela tionshi p to mech anical efficien cy. 

Introduc tion 

Force an d torque ma rgins are the fun ctional counte rparts of structural safety fact ors an d stress margin s.  Functio nal m argins as such are  relatively new, having b een instituted thre e decade s ago because of  failure s of l aunch vehi cle and  spacecraft mech anisms to  ope rate as intended. The defini tion of force   margi n relate s to the ratio betwe en the  driving fo rces and th e resi sting load s. If the d riving force i s greater  than the re sisting loa d, the mechani sm will start to move  with an  initial accele ration that is a function of   the magnitu de of the ma rgin. For exa mple, if the driv ing force i s twice the resisting load, the force  margin  is 100 p ercent. 

Typical spacecraft and l aunch vehi cle mech anism functions include d eployin g an a ntenna, relea sing a  launch restraint, rotating a  solar array, controllin g an antenn a poi nting me chanism , operating a valve, or  relea sing an interfa ce connector. T he drive  force or torque is typically provided by a spring -driven   actuato r, a p neumati c or hydrauli c piston, an ele ctromechani cal device such as a moto r or solenoid, o r  thermal exp ansion from an  expandin g wax actuator o r shap e memo ry alloy. 

The re sisting  force s or torque s typically  includ e fricti on from sliding su rfaces, beari ngs, and gea rs. Th e  internal fri ction and the stif fness of wire harnesses routed acro ss moving joints or interfa ces are a majo r  source of m echanical re sistance i n a deployable device. The type of friction of greate st con cern is static   friction (Co ulomb frictio n), which is usually somewhat greate r than t he sliding frict ion that follows the on set  of motion. Re sistin g loa ds can also be due to g ravity or a cceleration during th e launch phase. Valves may  have load s due to fluid pre ssure, an d sole noid a ctuated d evices may ha ve loads d ue to resi dual  magneti sm or a return spring. 

                                                       *The Aerospa ce Corp oratio n, El Segund o, CA 

Procee dings of the 37th Aeros pace Mec hanisms Sy mpos ium, Joh nson S pace F light Cent er, May 19-21, 2004 

© 2004 T he Aerospac e Corp oration  107