Explore linkage mechanisms by changing lengths

This is planar kinematics with rigid links and ideal pin/slider joints. Joint positions satisfy the geometric constraints at each time; velocities follow the position equations. Friction, clearance, deformation, collision and motor force/torque are not calculated.

Four-bars use one fixed assembly branch. The parallelogram is driven sinusoidally from 25° to 155°; speed is cycles/min. P lies 25 mm along the left normal from the midpoint of AB. Angles start at the rightward axis, positive counterclockwise. Travel ranges are approximate, sampled every 0.5° of drive phase.

The yellow line is the path for the current dimensions. Crossings in a 2D drawing do not verify physical clearances or out-of-plane layering. At a travel limit, playback stops rather than jumping to another assembly.

A four-bar crank-rocker turns rotation into a back-and-forth swing, as in a wiper-like motion. Even with uniform input, output speed changes. Adjust pivot spacing d and lengths a, b and c to inspect the output swing and the path of P.

Both input and output rotate in this four-bar example. Unlike a fixed gear ratio, the instantaneous angular-velocity ratio changes during a revolution. The example has a short ground link d. Changing the dimensions may prevent a full revolution.

Equal side arms and equal coupler/ground lengths keep the green coupler horizontal. Its path is an arc, so it moves sideways as well as vertically. This example drives the arms sinusoidally between 25° and 155°.

The rotating crank drives piston-like straight-line reciprocation. With the guide through the ground pivot, stroke is twice crank length a. Changing connecting-rod length b changes the positions and velocities between the endpoints.

The slider guide is displaced by height e from the ground pivot. With uniform input rotation, forward and return strokes take different times. Setting e to zero restores the in-line slider-crank. Some dimensions introduce angles that cannot be assembled.

The rotating pin slides vertically inside the slot while the yoke moves horizontally. Its position is x = a cos θ, giving sinusoidal travel at constant input speed. Switch to the slider-crank to compare their intermediate motion.