【正文】 (25) ? ? ? ?? ? ? ?yy07200 ， yayfyg ???? (26) and response equations ? ? ? ? 0s i nc o s 222525 ????? aayax ?? (27) ? ?? ? ? ?? ? 0s i nc os 2426216 ???????? aayaax ???? (28) The formulation enables the minimization of the different between the transversal displacement of the point C and the prescribed trajectory K. The result is the optimal values of the parameters a1， a2， a4. stochastic model of the hydraulic support The mathematical model (22) (28) may be used to calculate such values of the parameters a1， a2， a4， that the “difference between trajectories L and K” is minimal. However， the real trajectory L of the point C could deviate from the calculated values because of different influences. The suitable mathematical model deviation could be treated dependently on tolerances of parameters a1， a2， a4. The response equations (27) – (28) allow us to calculate the vector of response variables v in dependence on the vector of design variables u. This implies ? ?uhv ~? . The function h is the base of the mathematical model (22) – (28)， because it represents the relationship between the vector of design variables u and response v of our mechanical system. The same function h can be used to calculate the maximal allowed values of the tolerances 321 aaa ??? ， of parameters a1， a2， a4. In the stochastic model the vector u=[u1… un]T of design variables is treated as a random vector U=[U1… Un]T， meaning that the vector v=[v1… vm]T of response variables is also a random vector V=[V1? Vm]T， ? ?uhv ~? (29) It is supposed that the design variables U1? Un are independent from probability point of view and that they exhibit normal distribution， Uk~N(181。k, σk) (k=l， 2，?，n). The main parameters 181。k and σk (k=l， 2，?， n) could be bound with technological notions such as nominal measures， 181。k= 181。k and tolerances， . kk ?? 3?? ， so events kkkk U ???? ?????? ， k=l， 2，?， n (30) will occur with the chosen probability. The probability distribution function of the random vector V， that is searched for depends on the probability distribution function of the random vector U and it is practically impossible to calculate. Therefore， the random vector V will be described with help of “numbers characteristics”， that can be estimates by Taylor approximation of the function h in the point u=[u1… un]T or with help of the Monte Carlo method in the papers by Oblak (1982) and Harl (1998). 4. Numerical example The carrying capability of the hydraulic support is 1600 kN. Both fourbar mechanisms AEDB and FEDG must fulfill the following demand: they must allow minimal transversal displacement of the point C they must provide sufficient side stability The parameters of the hydraulic support () are given in Table 1. The drive mechanism FEDG is specified by the vector [b1+b2+b3+b4]T=[400， (1325+d)， 1251， 1310]T (mm) (31) And the mechanism AEDB by [a1+a2+a3+a4]T= [674， 1360， 382， 1310]T (mm) (32) In (31)， the parameter d is a walk of the support with maximal value of 925mm. Parameters for the shaft of the mechanism AEDB are given in Table 2. Optimal links of mechanism AEDB With this data the mathematical model of the fourbar mechanisms AEDB could be written in the form of (22) – (28). A straight line is defined by x=65(mm)() for the desired trajectory of the point C. That is why condition (26)is ? ? 065 7 ??? ax (33) The angle between links AB may vary between 176。 and 176。. The condition (33) will be discredited by taking into account only the points x1， x2， x19 in Table 3. These points correspond to the angles1921 222 … ??? ，， of the interval [176。，176。] at regular intervals of 1176。. The lower and upper bounds of design variables are u = [640， 1330 ， 1280 ， 0]T (mm) (34) u_ = [700， 1390， 1340， 30] T (mm) (35) The nonlinear programming problem is formulated in the form of (22) – (28). The problem is solved by the optimizer described by Kegl et al. (1991) based on approximation method. The design derivatives are calculated numerically by using the direct differentiation method. The starting values of design variables are [0a1， 0a2， 0a4， 0a7]T= [674， 1360， 1310， 30]T (mm) (36) The optimal design parameters after 25 iterations are u* = [676 .42， 1360 .74， 1309 .88， ]T (mm) (37) In Table 3 the coordinates x and y of the coupler point C are listed for the staring and optimal designs， respectively. Figure 4 illustrates the trajectories L of the point C for the starting (hatched) and optimal (full) design as well as the straight link K. Waterbased hydraulic systems Waterbased hydraulic systems traditionally have been used in hotmetal areas of steel mills. The obvious advantage of water system in these industries is their fire resistance. Water