Here it is assumed that the input link OA can be rotated in both directions, no matter whether full rotateability conditions are satisfied by the resulting dimensions or not。 In case full rotateability conditions are met with the design dimensions, the crank rotation proceeds in the same direction。 This would mean that, for instance, in applications involving cutting by means of the slider, functional efficiency would increase because of effective cutting action during both the forward and backward strokes in one cycle of motion。

4 Results and discussion

The function suitably selected for slider-velocity generation is y = x 0 ≤ x ≤ 1。 Computer program has been written to calculate the errors resulting from the design analysis of the slider-crank mechanism based on the procedure explained above。Wherever numerical integration is needed, Simpson’s rule [27] has been applied in the program。 In case Subdomain method is chosen, the numerical results thus obtained are those collected in Tables 1, 2。 Structural error distribution associated with the designs in Table 1, 2 are given in Fig。 5。 It is evident that the direction and amount of the crank rotation (±_ψ), choice of subdomains and the length of root-located interval (DEL) have varying degrees of effectiveness on the outcome。 All of the designs in Tables 1, 2 possess good dimensional quality。 As the amount of crank rotation decreases, the chances of getting better results increase。 The fact that multiplying slider displacement (_s) multiplies mechanism dimensions in the same proportion can be used to adjust the size to that needed。 Corresponding error distributions in the slider velocity of each design are depicted in Fig。 6。

If Galerkin method is applied on the same problem, results shown in Tables 3 and 4 are obtained。 Obviously the

Table 1 Slider-crank as y = x 0 ≤ x ≤ 1 generator by Subdomain method

Design No。 _ψ DEL (°) Subdomains Peak error

1 −90 1。0 0, 0。3, 0。55, 0。75, 0。9, 1。0 0。234E–1

2 −80 1。0 0, 0。3, 0。55, 0。75, 0。9, 1。0 0。315E–1

3 −60 1。5 0, 0。2, 0。4, 0。6, 0。8, 1。0 0。139E–1

4 50 1。9 0, 0。2, 0。4, 0。6, 0。8, 1。0 0。112E–1

Table 2 Slider-crank dimensions for designs in Table 1

Design No。 x1 x2 x3 ψ0 s0

1 0。4853 2。3994 1。9339 2。58 −0。9016

2 0。5755 2。6345 2。0800 1。76 −1。0154

3 −0。9808 4。6036 0。2067 106。50 −4。2616

4 −1。0539 5。5997 −1。6508 93。26 4。9628

Fig。 5 Structural error distributions in generating y = x 0 ≤ x ≤ 1 a by Subdomain method (Table 2)

Fig。 6 Velocity error distributions in generating y = x 0 ≤ x ≤ 1 by Subdomain method (Table 2)

Table 3 Slider-crank as y = x 0 ≤ x ≤ 1 Generator by Galerkin method

Design No。 _ψ DEL (°) Weighting func。 Peak error

1 80 1。9 Chebyshev poly。 0。643E–3

2 70 1。9 Chebyshev poly。 0。693E–2

3 −60 1。0 Chebyshev poly。 0。158E–2

4 −50 1。5 Chebyshev poly。 0。226E–3

Table 4 Slider-crank dimensions for designs in Table 3

Design No。 x1 x2 x3 ψ0 s0

1 −0。4288 3。0005 −2。5724 105。59 −0。1856

2 −0。6460 3。1413 −2。4984 7。23 1。1483

3 0。5663 4。0440 −3。4778 335。20 −1。0822

4 0。6101 5。0453 −4。4352 335。11 −1。3016

Fig。 7 Structural error distributions in generating y = x 0 ≤ x ≤ 1 by Galerkin method (Table 4)

quality of designs has risen appreciably relative to Subdomain method。 This is even clearer in Fig。 7, where the order of magnitudes as well as distributions of structural error in the motion domain are observed to be better。 Chebyshev polynomials w1 = x; w2 = 4x3 − 3x; w3 = 8x4 − 8x2 + 1; w5 = 16x5 − 20x3 + 5x have been considered as weighting functions, because they are known to possess orthogonal properties。 Consequently they have been found fit as suitable weighting functions。 The structural error and velocity error distributions are shown in Figs。 7, 8。 Precision-point or collocation method, when applied on the same problem, yields results seen in Tables 5 and 6。 The values of design parameters show some stability against changes in precision points, although their choice does have