b[jh[hl - uni-ruse.bgconf.uni-ruse.bg/bg/docs/cp15/2/2-4.pdf · >bgzfbdzgz\b[jh[hl b\zgemdzgh\
TRANSCRIPT
- 201 4 2
- -
Dynamics of a VibroBot: The mathematical model of a unidirectionally moving prototype of a mobile mechanical system with vibration propulsion is formulated. The results obtained from the numerical experiment with the robot dynamic model having linear elastic and dissipative characteristics are attached. The effects of variation of the robot’s parameters upon its dynamics were investigated and analyzed.
Key words: VibroBot, Vibrational drive, Mathematical Model, Dynamics, Numerical experiment.
--
-
-
-
- -
-
7 [ -
-
[7
XOZ OXYZ
-OY
m - -
G G2 - -
m X
G = m g - t)
x , x2, x , XOZ x , x2 x
x2 t) = x t) + l + t), x t) = x2 t) + l2 + t), - t) = t + ); l -, l2 , -
- 201 4 2
- -
V x t -
a 2x t2 V t, a2 2x2 t2 V2 t, a
2x t2 = a2 + 2 t 2 = a2 – 2 , = a r, -
- -
[ , -Gi, i = 2, …, ; Nj, Tj, j = 2; -Rv, v = 2, , Fk, Fb; l, l = 2, …, ; M , = Gi = mi g Fk = – k ,
= x2 – x + l Fk Fk = k s – l ), s x2 Fb = – b|V2 – V | –
Fb, V2 – V ) – l = – ml al M = – m r/ 2)a –
-
R , R2, R , P , P2, P , P , N , T , N2, T2 a , a2 -
l
a = Fa m + m + m a2 = m 2 – Fa) / m2 + m ),
a = a2 – 2 , R = – m a , R2 = m g, R = m2 + m )g,
l = l + {m [g l2 – l ) – a h2 – Fa h – h )} m2 + m )g, P = m a ,
V
l
x
N1 N2
T2 T1 G4 G5 O X
x C1 H2
H1
x2
b k
Z
R1
C2
r
V2 G2 G3
C V G1
2
Y
- 201 4 2
- -
P2 = {– Fah + m2 + m d – d ) + m d – d2 g – m a h d , P = m a , P = {Fah + m2 + m )d + m d2 g + m a h d , N = m g + {– Fah + m2 + m d – d ) + m d – d2 g – m a h d , T = m a , T2 = m a , N2 = m g + {Fah + [ m2 + m )d + m d2 g + m a h d ,
Fa = k x2 – x – l ) + b|V2 – V |
3
R1
R2
G3
a3
Fk
h
l2
l
l
C2
h
3
R2 R1
G2
Fba2 h2 2
h
d d
d
C h P1 P3P4P2
Fk
R3
G1
Fb
a1
d2
1
A B
4
r
P1P2
G4 D
T1a1
M4
N1
r G5
5
P4
E T2
a1
M5
N2
P3
- 201 4 2
- -
-
x t = V , x = , 2) V t = [k x2 – x – l ) + b|V2 – V | / [m + m + m V =
x2 t = V2, x2 = s ,
V2 t = m 2 t + ) – [k x2 – x – l ) + b|V2 – V | / m2 + m ), V2 =
) V = V t), V t) > ; V = V t)
)- ) t -
Nj = = t Nj t) > , j = 2 ,
- j Nj , -
-
[
)
,)ft
fttV
tV
V t t [t , tf t >
) K = P t) + P t) + R t) +,
t, P t) + P t) > R t) >
-
- ) -2), ) t tf B-
– – 2
m , m2 m x t), v t), a t)
- a t), a2 t), a t)
a t)
a t) a t) -
- 201 4 2
- -
– 2
2 –
- 2 ,e --
D = | T t) N t) |, 2 = = |T2 t) N2 t) |
- ,
-
l h l l2 r l m s x2 m2 d m d2 m d d = l + m d h k h2 b h h tf
, s , , b , k N V
k -
, , ,e) s
, , , )
– V -
- V
e, ,i, ) K
k K ,k) -
V ,k) k )
- 201 4 2
- -
e) )
- 201 4 2
- -
- 201 4 2
- -
i) )
K k
- 201 4 2
- -
-
- -
[ , i , 7 [2 ,
, [ , I I ,
, [ Y -
[
- , [
– [7
2–
[ –
[ B )
[
[
–
- , , -
@ - - ,
- - @ - - ,
- - @ -