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Add doc for transmission. Torque not handled. Check torque before PR.
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ethercat_driver_ros2/sphinx/user_guide/config_use_case_motor_with_gear_box.rst
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| Case study: motor coupled to a gearbox and a transmission screw with encoder | ||
| ============================================================================ | ||
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| This case study is a simple example to show how to set up the config of the :code:`EcCiA402Drive` generic plugin to take into account transmission parameters and encoder parameters. | ||
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| System configuration | ||
| -------------------- | ||
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| The system is composed of a motor coupled to a transmission line (a gearbox and a transmission screw) which rotation is measured by an encoder. | ||
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| Transmission configuration | ||
| ~~~~~~~~~~~~~~~~~~~~~~~~~~ | ||
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| The transmission is composed of a motor, a gearbox and a transmission screw with the following characteristics: | ||
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| - gearbox with gear ratio, reduction absolute: 57/13 (:math:`r \triangleq \frac{13}{57}`) | ||
| - transmission screw with lead: 1 mm (:math:`l \triangleq 1 mm`) | ||
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| Encoder configuration | ||
| ~~~~~~~~~~~~~~~~~~~~~ | ||
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| The encoder has the following characteristics: | ||
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| - Resolution (number of pulses/revolution): 500 CPR | ||
| - Encoder type: quadrature encoder | ||
| - Digital resolution (number of counts/revolution): :math:`\text{C} \triangleq 500\times 4 = 2000` | ||
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| Convert state values to physical values | ||
| --------------------------------------- | ||
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| The drive will transmit the following state values: | ||
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| - :code:`position` in :math:`\text{counts}` or :math:`c` | ||
| - :code:`velocity` in :math:`\theta` (revolutions per minute) | ||
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| We would like to have the following state values: | ||
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| - :code:`position` (:math:`d`) in :math:`\text{m}` | ||
| - :code:`velocity` (:math:`v`) in :math:`\text{m/s}` | ||
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| This is the configuration part of the tpdo of the :code:`EcCiA402Drive` plugin and corresponding to the :code:`state_interface` in ROS2 control terminology. | ||
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| Linear displacement per count of the encoder | ||
| ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ | ||
| The motor has a reductor so each turn of the motor does not correspond to a turn of the system. | ||
| It is necessary to first compute the rotation of the shaft at the output of the gearbox. | ||
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| * reduction absolute is :math:`r \triangleq \frac{13}{57}` | ||
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| So for 57 turns of the motor, the shaft will only turn 13 times. So the motor has to turn approximately 4.4 times to make the system turn once. | ||
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| The lead of the screw is defined as the linear distance traveled per rotation of the screw and in this case is :math:`1mm`. | ||
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| The encoder reports :math:`C \triangleq 2000` counts per revolution (CPR) so 2000 counts per turn of the shaft, so an angular resolution of :math:`\frac{360}{2000} = 0.18^{\circ}`. | ||
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| Let :math:`d` be the linear displacement in meters, :math:`r` the reduction absolute, :math:`l` the lead of the screw in meters and :math:`C` the counts per revolution of the encoder and :math:`c` the value of the encoder. | ||
| Then, a count :math:`c` of the encoder corresponds to a linear displacement :math:`d` of | ||
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| .. math:: | ||
| \begin{eqnarray} | ||
| c ~~\text{(in counts)} \longrightarrow d & = & r \times l \times \frac{c}{C} ~~\text{m}\\ | ||
| & = & \frac{13}{57} \times 10^{-3} \frac{c}{2000} ~~\text{m}\\ | ||
| & \approx & 0.000000114 \times c ~~\text{m} | ||
| \end{eqnarray} | ||
| The conversion factor is more precisely :math:`0.11403508771929824 \times 10^{-6}`. | ||
| So the displacement resolution, the displacement corresponding to one count of the encoder, is approximately :math:`0.114 µm`. | ||
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| The tpdo part of the configuration of the :code:`EcCiA402Drive` plugin will then be set up with the following values: | ||
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| .. code-block:: yaml | ||
| tpdo: # TxPDO = transmit PDO Mapping, slave (out) to master (in) (MISO), state values transmitted by the drive to ROS2 control | ||
| - index: 0x1a03 | ||
| channels: | ||
| - { | ||
| index: 0x6064, | ||
| sub_index: 0, | ||
| type: int32, | ||
| state_interface: position, | ||
| factor: 0.11403508771929824e-6, | ||
| offset: 0 | ||
| } # Position actual value | ||
| Convert velocity in :math:`\text{m/s}` from :math:`\text{rpm}` | ||
| ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ | ||
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| If the motor moves at a velocity of :math:`\theta` RPM, then the linear velocity :math:`v` in :math:`\text{m/s}` of the system is given by: | ||
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| .. math:: | ||
| \begin{eqnarray} | ||
| \theta ~~\text{(in rpm)} \longrightarrow v & = & \frac{13}{57} \times 10^{-3} \times \frac{1}{60} \times \theta ~~ \text{m/s} \\ | ||
| & \approx & 3.8011695906432747 \times 10^{-6} \times \theta ~~\text{m/s} | ||
| \end{eqnarray} | ||
| The tpdo part of the configuration of the :code:`EcCiA402Drive` plugin will then be set up with the following values: | ||
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| .. code-block:: yaml | ||
| tpdo: # TxPDO = transmit PDO Mapping, slave (out) to master (in) (MISO), state values transmitted by the drive to ROS2 control | ||
| - index: 0x1a03 | ||
| channels: | ||
| - { | ||
| index: 0x606c, | ||
| sub_index: 0, | ||
| type: int32, | ||
| state_interface: velocity, | ||
| factor: 3.8011695906432747e-6, | ||
| offset: 0 | ||
| } # Velocity actual value | ||
| Convert physical values to commands | ||
| ----------------------------------- | ||
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| This is the configuration part of the rpdo of the :code:`EcCiA402Drive` plugin and corresponding to the :code:`command_interface` in ROS2 control terminology. | ||
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| Command in counts to move by a certain distance in m | ||
| ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ | ||
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| To command the motor to move by a certain distance :math:`d` in meters, the number of counts :math:`c` to send to the motor is given by the formula: | ||
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| .. math:: | ||
| \begin{equation} | ||
| d \longrightarrow \text{c} = \frac{C}{rl} \times d \approx 8769.23076923077 \times d | ||
| \end{equation} | ||
| The 'rpdo' part of the configuration of the :code:`EcCiA402Drive` plugin will then be set up with the following values: | ||
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| .. code-block:: yaml | ||
| rpdo: # RxPDO = receive PDO Mapping, master (out) to slave (in) (MOSI), command values received by the drive from ROS2 control | ||
| - index: 0x1603 | ||
| channels: | ||
| - { | ||
| index: 0x607a, | ||
| sub_index: 0, | ||
| type: int32, | ||
| command_interface: position, | ||
| factor: 8769.23076923077, | ||
| offset: 0 | ||
| } # Target position | ||
| Command in rpm to move at a certain velocity given in m/s | ||
| ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ | ||
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| To command the motor to move at a certain velocity in m/s, the number of rpm to send to the motor is given by the formula: | ||
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| .. math:: | ||
| \begin{eqnarray} | ||
| v ~~\text{(in m/s)}\longrightarrow \theta & = & \frac{60}{rl} \times v ~~\text{(in counts)}\\ | ||
| & \approx & 263076.92307692306 \times v ~~\text{(in counts)} | ||
| \end{eqnarray} | ||
| The 'rpdo' part of the configuration of the :code:`EcCiA402Drive` plugin will then be set up with the following values: | ||
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| .. code-block:: yaml | ||
| rpdo: # RxPDO = receive PDO Mapping, master (out) to slave (in) (MOSI), command values received by the drive from ROS2 control | ||
| - index: 0x1603 | ||
| channels: | ||
| - { | ||
| index: 0x60ff, | ||
| sub_index: 0, | ||
| type: int32, | ||
| command_interface: velocity, | ||
| factor: 263076.92307692306, | ||
| offset: 0 | ||
| } # Target velocity | ||
| Complete configuration example for an EPOS4 drive | ||
| ------------------------------------------------- | ||
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| Note that we omit the ``offset`` parameter since their default value is equal to zero. | ||
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| .. literalinclude:: epos4_config_with_gear_box.yaml | ||
| :language: yaml | ||
| :caption: Example of a complete configuration for an EPOS4 drive with a gearbox and a transmission screw | ||
| :linenos: |
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