7.6 Straight Line Motion Mechanism -3

Straight Line Motion Using Swinging Block Mechanism :

Swinging block mechanism shown can be used for approximate straight line motion generation The coupler point G approximates a straight line and its displacement is also approximately a linear function of crank rotation.

The coupler point, G, can be on a straight line only at six positions. The maximum deviation, x, is minimised using Chebyshev Theorem (which is beyond the topic). This procedure yields the relations between the link lengths, stroke s, corresponding crank rotation y, and the maximum deviation x. Using the nomenclature given on the figure these equations are:

The above equations can be represented in a chart form as shown in Chart 5. p represents the maximum deviation of the actual motion of point C from the linear functional relationship with respect to the crank rotation

Example

We want to design a swinging block mechanism for straight line motion where s=100 and the corresponding crank rotation =150⁰

Abak 5 den , =150⁰ için: d/a 1.74; s/a 4.65; h/a 6.3; f/a 7.3; p 0.24 % (strokun yüzdesi olarak). s=100 mm için yaklaşık değerler olarak: a 21.51 mm; h 135.48 mm; f 156.99 mm; d 37.20 mm; x0.02 mm elde edilir.

d/a =1.735 ve s =100 mm kullanılarak denklemler çözüldüğünde:

a = 21.94; h = 140.43 mm; f = 162.35 mm; d = 38.07 mm; =151.26⁰; = 52.71⁰ olarak bulunur.

If one requires the angle to be exactly 150⁰, different d/a ratios can be tried (or one can construct a different solution algorithm) to obtain a more accurate result( try d/a=1.7390 ). For such a trial and-error method one can very effectively use "Goal Seek" tool in Excel "Tools" menu.

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