5441336905

514

J. Giergiel, W. Żylski

N_uN₂

fl,f2

M₂

Z, Zj, l₂, h\

r i = r₂

r

loads applied to corresponding wheels coefficients of rolling friction of corresponding wheels driving torąues

corresponding distances resulting from the system geometry, h\ = riZf¹ radii of corresponding wheels.

The above eąuations do not take into account the smali mass of wheel 3 and rolling friction of this wheel.

While analysing converse the dynamical problem, if the kinematic para-meters of motion are known, it is possible to determine the driving torąue and the multipliers out of the derived eąuations of motion. On account of the found form of the right-hand sides of these eąuations, it is advantageous to introduce a transformation for decoupling the multipliers from the torąues (Żylski, 1996). Aiming at this, eąuations (1.5) should be expressed in a matrix form

M{q)q + C(q,q)q = B(q)-r + J^T(g)A    (1.6)

The matrices M. C and B present in the above eąuations result from dynamical eąuations of motion (1.5). The vector of coordinates q can be decomposed as

9 = [<7l>92]^T    q£R", q₁SR^Tn, q₂eRⁿ~^m (1.7)

In this case, eąuation of constraints (1.1) is given in the form

[Ji(9), J₂(g)]

91

92

= 0

det Ji(g) 0

(1.8)

The vector q₂ should be selected in such a way so that its size would corre-spond to the number of degrees of freedom and so that det J i (q) ^ 0. In such a case

Jl2(<?)

In—m

92 = T(q)q₂

9 = ^(9)92 +7X9)92    (1-9)

where J12 = — Jj ¹(g)J2(g), and l_n__m stands for the identity matrix. In this case, dynamical eąuations of motion (1.6) can be put down in the form

(1.10)

Mn(q)q₂ + Cu(q.q)q₂ = Bi{q)r + ij (q)X M₂₂(q₂)q₂ + C₂₂(q₂q₂)q₂ = B₂(q₂)T

The structure of matrices present in eąuations (1.10) is described in the work by Żylski (1996). Obtained eąuations (1.10) show the so-called reduced