u r u RO A u Lu  u L ()v   。 (16) Based on Eq。 (16), the relation between error of link and

where the material of all links is identical, so the elastic modulus E of all links also is identical。 For convenience of dynamic analysis, the section area Si is approximately a con- stant, namely, the section area does not change along the link- age。

Substituting Eq。 (20) into Eq。 (17), the dynamic equation can be written as

position error of main slider 8 can be obtained as

 

(i = 51,52,53,54,    j = 91,92,101,102)。

The force analysis of the under link is shown in Fig。 7, where pi = mi g/l is the distribution force that the gravity acts on link; qi = mi aci /l is distribution force that inertia force acts on link。

Taking hinge joint Oi as the origin, the axial force Fl with the distance being x between the pivot joint Oi and force bear- ing point is given by

Fl    ui [Fi  pi (l x) qi (l x)] 。 (18)

Eq。 (21) contains four equations, but the number of un- known variables is three:x ,y and。 Therefore, one sup- plementary equation is provided。 Combining the equations by D’Alembert principle, the dynamic model of over-constrained mechanism that can be solved is obtained。

4。 Simulation results and model verification

Dynamic modeling method is applied to the transmission mechanism of YHK-60 type multi-linkage high-speed press machine, shown in Fig。 8。 According to the structure  parame-

Table 1。 Kinematic parameters。

Fig。 9。 Strain test of components: (a) The link l41  pasted strain  gauges;

(b) the link l51 pasted strain gauges; (c) strain test site。

Fig。 8。 YHK-60 type multi-linkage high-speed press machine。

ters and kinematic parameters shown in Table 1, the dynamic model is simulated by Matlab when the stamping velocity is 500 spm (strokes per minute)。

To prove the results the authors acquired, the strain gauges are pasted on the corresponding site of main moving elements,文献综述

Based on the material mechanics, the axial force can be written as

whereis the tensile strain (or compressive strain), S41 = S42 =

frame and beam before assembly。 The factors that are the  po-

8。2×10-3m2, S= 14。6×10-3  m2 and E = 2。1×1011 pa。

sition of strain gauges on link, strength of wire and corrosion of lubricating oil are considered。 The link pasted strain gauges are shown in Figs。 9(a) and (b)。 To enhance the reliability of testing, the full-bridge is applied。 If one or two strain  gauges of the four are broken during the assemblage (but they cannot be on the same side of linkage), the surplus of strain gauges

The constraint forces of l41, l42, l51 and l52  are converted  to an axial force by using Eq。 (18), and then comparing it with test data to verify the correctness of dynamic model。

Fig。 10 shows the contrast between experimental data and theoretical value of dynamic model of upper link。  Based on the data, the significance test is calculated with the r test。  The

can form a half-bridge to test。

coefficient of determination (r2) of link l

is 0。753。 The coef-

 The strain test platform was put up by using Labview  soft-ficient of determination (r2) of link   lis 0。684。 We find  that

ware。 In the NI test system, the type of embedded controller is PXI-8187 with the crate PXI-1042Q。 The type of high-speed multifunction data acquisition devices is PXI-6251。 The  type of SCXI chassis is SCXI-1000 with SCXI adapter SCXI-1349。 And the type of universal strain gage input module is SCXI- 1520 with the front-mounting terminal block SCXI-1314, shown in Fig。 9(c)。