Development of constant output–input force ratio in slider–crank mechanisms

Figures & data

Figure 1. Ice cutting process.

Figure 2. Slider–Crank feeding mechanism.

Figure 3. Velocity diagram.

Figure 4. Q – θ relationship for several constant input force W′ values.

Figure 5. W′ – θ relationship for several constant output pushing force Q values.

Figure 6. Kinematic diagram of slider–crank feeder mechanism with a spiral spring at point O.

Figure 7. Block diagram of the control system.

Figure 8. The relationship between the selected θ ₁ and Q _net Error Percentage.

Figure 9. The slider–crank feeder mechanism inclined with an angle φ.

Figure 10. The user interface of force control in slider–crank feeder mechanism.

Table 1. W–input values for manual control process.

θ 0 (º)	Q (N)	W′ (kg)	W′–input (kg)
45	300	48.57	49
44	300	46.94	47
43	300	45.34	45.5
42	300	43.78	44
41	300	42.26	42.5
40	300	40.76	41
39	300	39.30	39.5
38	300	37.87	38
37	300	36.46	36.5
36	300	35.08	35.5
35	300	33.73	34
34	300	32.40	32.5
33	300	31.09	31.5
32	300	29.80	30
31	300	28.53	29
30	300	27.27	27.5
29	300	26.04	26.5
28	300	24.82	25
27	300	23.61	24
26	300	22.42	22.5
25	300	21.24	21.5
24	300	20.08	20.5
23	300	18.92	19
22	300	17.78	18
21	300	16.64	17
20	300	15.52	16

Figure 11. Error percentage – θ relationship obtained using manual control method for Q = 300 N.

Figure 12. Error percentage – θ relationship obtained by offsetting Q _net value.

Table 2. The parameters used in the application of a controller.

Name of graph	Spring constant (Nm/rad)	Piston force due to spring (N)	Net error-free pushing force (N)	θ 0 (º)	θ 1 (º)	θ2 (º)
e–25	k–25	Q k–25	$Q_{\text{net}}^{*}$–25	20	25	45
e–30	k–30	Q k–30	$Q_{\text{net}}^{*}$–30	20	30	45
e–32.5	k–32.5	Q k–32.5	$Q_{\text{net}}^{*}$–32.5	20	32.5	45
e–35	k–35	Q k–35	$Q_{\text{net}}^{*}$–35	20	35	45
e–40	k–40	Q k–40	$Q_{\text{net}}^{*}$–40	20	40	45

Table 3. The parameters calculated in control application.

Graph name	$Q_{\text{net}}^{*}$ (N)	k (Nm/rad)	${\theta }_0^{*}$ (º)
e–25	61.44	67.29	48.31
e–30	57.50	64.66	50.21
e–32.5	55.59	63.39	51.19
e–35	53.73	62.15	52.18
e–40	50.14	59.76	54.20

Figure 13. Variation of net pushing forces developed by a constant 100 N load and five different springs in the operation interval.

Figure 14. Variation of per cent error in the net pushing force developed by a constant 100 N load and five different springs in the operation interval.

Table 4. The equal error parameters.

e max curve		e min curve
θ 1 (°)	44.9	θ 1 (°)	20.1
θ a (°)	27	θ b (°)	36
emax (N)	303.7	emin (N)	297.7

Figure 15. Angle θ ₁ calculated using Equal Error Distribution Method and the resulted Q _net values.

Figure 16. Piston pushing force vs. crank angle.

Figure 17. The slider–crank mechanism inclined (a)+90° and (b) −90°.

Table 5. Calculated values for the general case applications.

φ (°)	90	−90
k (Nm/rad)	356.44	318.36
${\theta }_0^{*}$ (°)	49.94	50.51
Q net (N)	300	300
W (N)	602.60	543.30

Figure 18. The slider–crank feeder mechanism simulated in SolidWorks.

Figure 19. Comparison of Q _net values obtained by SolidWorks simulations and the developed user interface.