==========
Belt drive
==========

Belt drive link properties implement a toothed belt drive. Only the linear elastic behaviour is modelled, non-linearities are neglected. The simplifications are:

- the belt is always considered prestressed (both strands are contributing to the stiffness)
- the prestress force is not modelled and has to be added as load in an analysis if desired
- irregular transmission due to the teeth is not modelled
- local deformation of the pulleys is not modelled

----------
Definition
----------

Source and target interfaces should be chosen as shown in following figure:

   .. image:: media/lp_belt.png
      :alt: Belt drive link definition
      :scale: 100 %


^^^^^^^^^^^^^^^^^^^^
Source interface
^^^^^^^^^^^^^^^^^^^^

==============  ===========================================================================================
Type            Stationary interface (6dof)
Topologies      Peripheral face of the source pulley
Location        Center of the source pulley
u direction     Axial, along the axis of rotation of the source pulley
v direction     Pointing towards the center of the target pulley
w direction     Resulting direction
==============  ===========================================================================================

^^^^^^^^^^^^^^^^^^^^
Target interface
^^^^^^^^^^^^^^^^^^^^

==============  ===========================================================================================
Type            Stationary interface (6dof)
Topologies      Peripheral face of the target pulley
Location        Center of the target pulley
u direction     Axial, along the axis of rotation of the target pulley
v direction     Aligned with the v-direction of the source interface
w direction     Parallel to the w-direction of the source interface
==============  ===========================================================================================

^^^^^^^^^^^^^^^^^^^^^^^^^
Recommended link settings
^^^^^^^^^^^^^^^^^^^^^^^^^

==========================  ==========================
Use ground for source       unchecked
Location master             none
Orientation master          either source or target
==========================  ==========================

----------
Parameters
----------

===================  =========  ===========  ==============================================================
Parameter            Unit       Symbol       Description
===================  =========  ===========  ==============================================================
Source gear radius   m          :math:`r_S`  Radius of the pitch line of the source pulley
Target gear radius   m          :math:`r_T`  Radius of the pitch line of the target pulley
Belt stiffness       N/m        :math:`k`    Stiffness of one strand of the belt including tooth compliance
Belt damping         Ns/m       :math:`d`    Damping coefficient of one strand of the belt
===================  =========  ===========  ==============================================================

The stiffness of the belt can be calculated using the specific stiffness :math:`c_{st}`, the width of the belt :math:`b`, and the free lenght of a strand :math:`l_{1}` according to :math:`k = c_{st} \, b / l_1`.