On Biomimetics by Lilyana Pramatarova

112 On Biomimetics

0

0

010

0

0

0

001

0) ,

2

3

• ,
  2

1

-( : 0), ,

2

3

2

1

-( : 0), 0, ,( : 0), 0, (0, :



















 

































 





 



 





coscossinsincos

cossincossinsin

cos sin

sin cos

cos sin

cossin

sincos

r r,r rr

1

1P

13 P P

1P

12 P P

1P

P11

1P

1P

1P

R

O P P P

And,

1,2,3)1P i1' 1P 1 1PPRP i1 (i (3)

Therefore, the coordinate of each element of P^1 P 1 i’ is:

)

2

3

2

,^1

2

3

2

,^1

2

( :^1

)

2

3

2

1

,

2

3

2

1

,

2

1

( :

,( : , )

   

   



sinsinrcosr' sincosrcosr sinr

sinsinrcosr' sincosrcosr sinr

sincosrsinsinrcosr'

13 P P P P P

1P

12 P P P P P

1P

P11 P P

1P

   

   



P

P

P

(4)

Next, P 1 i’, B 1 i’in OB 1 - XYZ, i.e. B^1 P 1 i’ and B^1 B 1 i’ can be defined as:

1,2,3)( 0, 0,

0) ,

2

,^3

2

( : 0), ,^1

2

,^3

2

( : 0), 0, ,( :^1

 

 

i'h''

r rr rr

T

i1 1

1P

i1

1B

13 B B

1B

12 B B

1B

B11

1B

PP

B B B

So, each element of B^1 P 1 i’ can be expressed as:

)

2

3

2

,^1

2

3

2

,^1

2

( :^1

)

2

3

2

,^1

2

3

2

,^1

2

( :^1

,( : - , )

sinsinrcosr' 'hsinrsincosrcosr

sinsinrcosr' sincosrcosr 'hsinr

'hsincosrsinsinrcosr'

13 P P P P P 1

1B

12 P P P P P 1

1B

P11 P P 1

1B

    

    



   

   



P

P

P

(7)

Accordingly, the length of each actuator can be defined:

 i1 i''l 1,2,3)(

1B

i1

1B

i^ BP^ (8)

By Equation (5), (7) and (8), the equations describing the relation between the lengths of
pneumatic actuators, wires attached in Segment 1, Backbone 1, and the angles of two revolute
joints can be defined as follows:

(^)  1 2   
22 2
l'  rrrPBPcos- sin sin -rPcos sin h 1 '^
(1)
(2)
(5)
(6)