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Bevel Gear Constraint

Kinematic constraint for transferring rotational motion at a fixed ratio about arbitrarily oriented axes

Library

Gears and Couplings/Gears

Description

This block represents a bevel gear constraint between two frames. The constraint restricts motion such that rotation of the base frame causes rotation of the follower frame and vice-versa. The two frames spin as meshed gears about the individual Z axes, each aligned with a bevel gear shaft.

The two shafts can lie at an arbitrary angle to each other. This angle, always between 0° and 180°, corresponds to a configuration in which the two +Z axes are either parallel or converging toward each other. At 90° the two shafts are perpendicular. At 0°, the two gears are parallel and the bevel gear functions as a spur gear.

During simulation, the remainder of the mechanism must hold the gears in alignment. The gear shafts must lie at the distance and angle specified in the block dialog box. The distance between the base and follower frame origins, which represent the two gear shafts, follows from the law of cosines:

where:

  • D is the distance between the two frame origins.

  • RB, RF are the pitch radii of the base gear and follower gears.

  • θ is the angle between the base and follower gear shafts.

Bevel gear Schematic

Dialog Box and Parameters

The block dialog box contains a Properties area with bevel gear options and parameters.

Base Gear Radius

Enter the pitch circle radius of the base gear. This is the radius at which the base gear teeth contact the follower gear teeth. Select a physical unit. The default is 10.0 cm.

Follower Gear Radius

Enter the pitch circle radius of the follower gear. This is the radius at which the follower gear teeth contact the base gear teeth. Select a physical unit. The default is 10.0 cm.

Shaft Axes

Select the relative orientation between the spinning shafts of the base and follower gears. Options include Perpendicular and Arbitrarily Oriented:

  • Perpendicular — Orient the two spinning shafts at a right angle to each other. This is the default setting.

  • Arbitrarily Oriented — Orient the two spinning shafts at a general angle to each other. Selecting this option exposes an additional parameter.

    Angle Between Shafts

    Enter the angle between the spinning shafts of the base and follower gears. Select a physical unit. The default value is 90 deg.

Ports

The block contains frame ports B and F, representing base and follower frames, respectively.

See Also

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