# 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:

• An eccentric cam

• A 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 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```, which ignores losses to allow for HIL-capable computation times.

• `Constant efficiency`, which is the default friction setting for block versions prior to R2020b. In this case, you specify a component efficiency that remains constant throughout the simulation

• `Temperature-dependent efficiency`, which models temperature-dependent component efficiencies by creating a 1-D lookup table based on the Temperature vector and the given component efficiency vector. This setting also,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's Thermal mass parameter.

### Thermal Model

You can model the effects of heat flow and temperature change by enabling the optional thermal port. To enable the port, set Friction model 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.

## Ports

### Conserving

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Rotational mechanical conserving port associated with the base shaft.

Rotational mechanical conserving port associated with the follower shaft.

Thermal conserving port associated with heat flow.

#### Dependencies

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

## Parameters

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### Main

Total number of teeth projecting outward from the cycloidal disk perimeter. This quantity should be less 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 quantity should be greater 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.

Vector of temperatures used to construct 1-D temperature-efficiency lookup tables. Values of the vector elements must increase from left to right. The number of elements in the vector must match the number of elements in the vectors specified for these parameters:

#### Dependencies

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

Torque transfer efficiency 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.

How you specify the efficiency values depends on which Friction model you select:

• `Constant efficiency` — Specify the value as a scalar.

• ```Temperature-dependent efficiency```— Specify the value as a vector in which each element is the ratio of output power to input power at the corresponding the temperature element in the temperature vector. The number of elements in the vector must match the number of elements in the vectors specified for the Temperature parameters.

#### Dependencies

This parameter is available when you set Friction model to ```Constant efficiency``` or ```Temperature-dependent efficiency```. 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.

How you specify the efficiency values depends on which Friction model you select:

• `Constant efficiency` — Specify the value as a scalar.

• ```Temperature-dependent efficiency```— Specify the value as a vector in which each element is the ratio of output power to input power at the corresponding the temperature element in the temperature vector. The number of elements in the vector must match the number of elements in the vectors specified for the Temperature parameters.

#### Dependencies

This parameter is available when you set Friction model to ```Constant efficiency``` or ```Temperature-dependent efficiency```. For more information, see Thermal Model.

Absolute value of the cycloidal disk power above which the full efficiency factor applies. Below this value, a hyperbolic tangent function smooths the efficiency factor.

When you set Friction model to `Constant efficiency`, a hyperbolic tangent function smooths the efficiency factor to one, such that the efficiency losses go to zero at the resting state.

When you set Friction model to `Temperature-dependent efficiency`, 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.

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 raise the computational cost of simulation.

### Thermal Port

To enable these settings, set Friction model to `Temperature-dependent efficiency`. For more information, see Thermal Model.

Thermal energy required to change the component temperature by a single temperature unit. 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

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