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Kinematic constraint for transferring rotational motion at a fixed ratio about parallel axes
This block represents a common gear constraint between two frames, base and follower. The constraint restricts motion, forcing the frames to spin in sync. Each frame, possessing at least one rotational degree of freedom, spins about its individual Z axis.
To assemble, the common gear constraint imposes several restrictions on the relative position and orientation of the port frames. Through blocks such as Rigid Transform, Joints, and Constraints, the remainder of the model must provide the geometric and kinematic relationships to satisfy these restrictions:
The Z axes of the base and follower frames must point in the same direction.
The X and Y axes of the base and follower frames must be in the same plane.
The common gear constraint can be internal or external. If the constraint is internal, the base and follower gear shafts spin in the same direction. If it is external, the shafts spin in opposite directions. The tooth ratio between the two gears determines the magnitude of the angular velocity ratio:
$$\left|\frac{{\omega}_{F}}{{\omega}_{B}}\right|=\frac{{N}_{B}}{{N}_{F}}=\frac{{R}_{B}}{{R}_{F}},$$
where:
ω_{B} and ω_{F } are the angular velocities of the base and follower gears.
N_{B} and N_{F} are the tooth numbers of the base and follower gears.
R_{B} and R_{F} are the pitch radii of the base and follower gears. These are the radii of the gear pitch circles, imaginary circles tangent to each other at the tooth-tooth contact point.
Gear Frames and Dimensions
The block dialog box contains a Properties area with common gear options and parameters.
Select gear type. Options include internal or external. Internal gears have teeth along the inner circumference. External gears have teeth along the outer circumference. The default type is External.
Select the method to specify the common gear with. Options include Center Distance and Ratio and Pitch Circle Radii.
Specify the common gear constraint in terms of the center-to-center separation distance and the gear teeth ratio (Nf/Nb).
Enter the center-to-center distance between base and follower gears. Select a physical unit. The default value is 20.0 cm.
Enter the gear teeth ratio between base and follower gears. This ratio is Nf/Nb, where Nf and Nb represent the number of teeth in the follower and base gears, respectively. The default value is 1.0.
Specify the common gear in terms of the base and follower gear radii.