Substitute F into Equations B-2 and B-3 and solve for a and b 



M d 

 ^ 4 e T„ 



(B-4) 



M d 

 ^ = 2~717 



Since the guide frame length must be S from Figure B-lf, we have 



2 



(B-5) 



o2 2 , 

 S = e + 



(H^) 



(B-6) 



Substitute Equations B-4 and B-5 into Equation B-6 and solve for e 



2 



2 2 



S = e + 



/ M d M d \ 



\4 e T„ 2 e W/ 



4 c2 2 _^ 



e - S e + 



MdW+2MdT 

 8 W T„ 



= 



2 S 



The angle of rotation is 



Entanglement occurs when 



(ir 



2 /MdW + 2MdT, 



8 W Tc 



e = 2 tan 



-1 a + b 



Z e 



(b¥f^)^ (« - ^ V > (if 



If Equations B-1 and B-2 are not simplified, more complicated nonlinear 

 equations will be derived; and numerical methods are needed to solve the 

 unknowns a , b , and e . 



32 



