507 Mechanical Movements

178

Contrivance for varying the speed of the slide carrying the…

Contrivance for varying the speed of the slide carrying the cutting tool in slotting and shaping machines, etc. The driving-shaft works through an opening in a fixed disk, in which is a circular slot. At the end of the said shaft is a slotted crank. A slide fits in the slot of the crank and in the circular slot; and to the outward extremity of this slide is attached the connecting-rod which works the slide carrying the cutting tool. When the driving-shaft rotates the crank is carried round, and the slide carrying the end of the connecting-rod is guided by the circular slot, which is placed eccentrically to the shaft; therefore, as the slide approaches the bottom, the length of the crank is shortened and the speed of the connecting-rod is diminished.

Only the input is driven; every other part of this model moves by physics (MuJoCo), and its ratios are measured. Run it live, change its parameters, or switch the friction off to see the output stop.

Modelled as
The slotted crank (the one driven joint, 20 rpm) carries a pin in its slot, by real contact. The same pin runs in a circular slot (radius 6 cm, 1.4 cm wide) cut in a fixed disk behind the crank, whose centre is 2.5 cm from the shaft, so the pin runs 3.5 to 8.5 cm from the shaft. A 16 cm connecting-rod from the pin works the tool slide in its guides. No gravity (a plan). gen178.py.
Measured
The tool slide follows the crank at +0.086, -0.041, -0.035 and -0.032 m/rad in four windows (kinematic +0.0857, -0.0402, -0.0347, -0.0321, r2 at least 0.996). It goes 12.3 cm, from -3.9 to +8.4 cm; the pin shortens the crank to 3.5 cm at the bottom and slows the slide there. Penetration 0.03 mm after settling.
Notes
The pin is held in both slots by contact, no pin joints. The circular slot is a ring of 96 flat segments around an island disc. The driver is a soft servo (kv 2) so that the crank still turns at speed when its slot is switched off in the control.

Film (MP4) · GIF · Still (PNG) · Spec (YAML) · Model (MJCF)

Figure 178 from Brown, 1868
Brown's figure 178 (1868)