# Cycloidal Drive

High-ratio speed reducer based on cycloidal disk motion

• Library:
• Simscape / Driveline / Gears

## Description

The Cycloidal Drive block represents a compact, high-ratio, speed-reduction mechanism that contains four key components:

• Eccentric cam

• Cycloidal disk

• Ring-gear housing

• Pin rollers

The eccentric cam, which extends from the base shaft, sits inside the cycloidal disk. This disk meshes with the ring-gear housing. The pin rollers, which extend from the follower shaft, sit in matching holes on the cycloidal disk.

During normal operation, the base shaft drives the eccentric cam. The cam spins inside the cycloidal disk, causing it to rotate in an eccentric pattern about an offset axis. As it moves, the cycloidal disk engages the internal teeth of the ring-gear housing. The internal meshing reverses the rotational velocity direction.

Pin rollers extending from cycloidal disk holes transmit rotational motion to the follower shaft. This shaft spins counter to the base shaft at a highly reduced speed. The large reduction ratio results from the near-equal cycloidal disk and ring gear tooth numbers. The effective gear reduction ratio is

`$r=\frac{{n}_{R}-{n}_{C}}{{n}_{C}},$`

where:

• r is the gear reduction ratio.

• nR is the number of teeth on the ring gear.

• nC is the number of teeth on the cycloidal disk.

The gear reduction ratio constrains the angular velocities of the base and follower shafts according to the expression

`${\omega }_{F}=-r{\omega }_{B},$`

where:

• ωF is the angular velocity of the follower shaft.

• ωC is the angular velocity of the base shaft.

The gear reduction ratio also constrains the torques acting on the base and follower shafts, according to the expression

`${T}_{B}=r{T}_{F}+{T}_{f},$`

where:

• TB is the net torque at the base shaft.

• TF is the net torque at the follower shaft.

• Tf is the torque loss due to friction. For more information, see Model Gears with Losses.

The figure shows the cycloidal drive in front and side views. The kinematics of the drive system cause a reversal of the base and follower shaft angular velocities so that the two shafts spin in opposite directions.

The cycloidal drive can operate in reverse mode, that is, with power flowing from the follower shaft to the base shaft. In the reverse mode, torque transfer efficiencies are typically negligible. You can adjust the efficiency by changing the value of the Efficiency from follower shaft to base shaft parameter.

### Friction Model

You can set the meshing losses friction model to:

• ```No meshing losses - suitable for HIL simulation```.

• `Constant efficiency`, which is the default friction setting for block versions prior to R2020b.

• `Temperature-dependent efficiency`, which models variability in the base-shaft efficiencies calculated in the `Constant efficiency` setting according to a user-supplied look-up table. The temperature-dependency setting enables a thermal conserving port H. This port receives the heat flow into the block, which is translated into the block temperature according to the gear Thermal mass.

### Thermal Model

You can model the effects of heat flow and temperature change by exposing an optional thermal port. To expose the port, in the Meshing Losses tab, set the Friction model parameter to ```Temperature-dependent efficiency```.

### Variables

Use the Variables settings to set the priority and initial target values for the block variables before simulating. For more information, see Set Priority and Initial Target for Block Variables.

Dependencies

Variable settings are exposed only when, in the Meshing Losses settings, the Friction model parameter is set to `Temperature-dependent efficiency`.

## Ports

### Conserving

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Rotational conserving port representing the base shaft.

Rotational conserving port representing the follower shaft.

Thermal conserving port associated with heat flow.

#### Dependencies

This port is enabled when Meshing Losses is set to ```Temperature-dependent efficiency```.

## Parameters

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### Main

Total number of teeth projecting outward from the cycloidal disk perimeter. This number should be slightly smaller than the number of teeth or pins on the ring gear. The ratio of the gear tooth numbers defines the relative angular velocities of the base and follower shafts.

Total number of teeth or pins projecting inward from the ring gear housing. This number should be slightly larger than the number of teeth on the cycloidal disk. The ratio of the two gear tooth numbers defines the relative angular velocities of the base and follower shafts.

### Meshing Losses

• ```No meshing losses — Suitable for HIL simulation``` — Gear meshing is ideal.

• `Constant efficiency` — Transfer of torque between worm and gear is reduced by friction.

• `Temperature-dependent efficiency` — Torque transfer is determined from user-supplied data for meshing efficiency and temperature.

Array of temperatures used to construct 1-D temperature-efficiency lookup tables. The array element values must increase left to right. The number of elements in the array must match the number of elements in the arrays specified for these parameters:

#### Dependencies

To enable this parameter, set Friction model to ```Temperature-dependent efficiency```.

Torque transfer efficiency in normal operation mode, that is, with the base shaft driving the follower shaft. Efficiency values must fall in the interval [0, 1]. Larger efficiency values correspond to greater torque transfer between the base and follower shafts. Values approaching unity are typical.

For the

• Non-thermal model — Specify the value as a scalar.

• Thermal model — Specify the value as an array in which each element is the ratio of output power to input power at the corresponding the temperature element in the temperature array. The number of elements in the array must match the number of elements in the arrays specified for the Temperature parameters.

#### Dependencies

This parameter is specified as an array when you select a thermal model. For more information, see Thermal Model.

Torque transfer efficiency in reverse operation mode, that is, with the follower shaft driving the base shaft. Efficiency values must fall in the interval [0, 1]. Larger efficiency values correspond to greater torque transfer between the base and follower shafts. Values approaching zero are typical.

For the

• Non-thermal model — Specify the value as a scalar.

• Thermal model — Specify the value as an array in which each element is the ratio of output power to input power at the corresponding the temperature element in the temperature array. The number of elements in the array must match the number of elements in the arrays specified for the Temperature parameters.

#### Dependencies

This parameter is specified as an array when you select a thermal model. For more information, see Thermal Model.

Absolute value of the cycloidal disk power above which the full efficiency factor applies.

For the non-thermal model, when power is below the specified value, a hyperbolic tangent function smooths the efficiency factor to one, such that the efficiency losses go to zero at the resting state.

For the thermal model, a hyperbolic tangent function smooths the efficiency factor between zero when at rest and the value provided by the temperature-efficiency lookup table when at the specified power threshold.

As a guideline, the power threshold should be lower than the expected power transmitted during simulation. Higher values can cause the block to underestimate efficiency losses. However, very low values may increase the computational cost of simulation.

### Thermal Port

These settings are exposed when you select a thermal model. For more information, see Thermal Model.

Thermal energy required to change the component temperature by a single degree. The greater the thermal mass, the more resistant the component is to temperature change.

#### Dependencies

To enable this parameter, set Friction model to ```Temperature-dependent efficiency```.

Component temperature at the start of simulation. The initial temperature alters the component efficiency according to an efficiency vector that you specify, affecting the starting meshing or friction losses.

#### Dependencies

This parameter is exposed when you select a thermal model. For more information, see Thermal Model.