The mechanism shown is a gimbal, which is used to stabilise cameras during video use.

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The mechanism shown is a gimbal, which is used to stabilise cameras during video use.

The gimbal can control orientation in three directions, with each orientation controlled by a small motor. Typically, the gimbal contains a small gyro sensor in the last link which is used to measure the motion of the
platform.

The gimbal can be operated in several modes – typical modes of operation might include:

  • Pan-follow: the gimbal will smooth out panning motion (rotation about the yaw axis) while keeping the vertical orientation (pitch angle) and roll angle constant. In other words, any jerkiness of motion by the operator panning the camera is smoothed out.
  • Constant: the gimbal will keep the camera facing in a fixed orientation (pitch and yaw kept constant). In this mode, a joystick or d-pad on the gimbal can be used to pitch or yaw smoothly.

When a gimbal is initially set up, the camera is placed on the platform and its position adjusted so that its centre of mass is centred at the intersection of the axes so that it will sit in any orientation – this will minimise the effort for the axis drives during operation.

This model has the revolute axes used to stabilise the camera. The above model contains several prismatic joints corresponding to adjustable mountings used to centre the camera’s centre of mass.

Model

 

You have been provided with an assembly, created in Solidworks, giving a slightly simplified representation of the gimbal. You have also been provided with a Simscape Multibody model created with the Solidworks/Simscape translator. This translator provides an XML file containing the topology and STEP files containing precise 3D geometry for each body.

For your model, you will need to ensure that a camera of a given mass and centre of mass is placed on the platform and balanced.

Tasks

  1. Create a kinematic description of the location of the camera mounting point using the specific settings given. You can use Denavit-Hartenberg matrices, quaternions or any other method you feel will work. You should be able to calculate the location of this point based on a given set of angles.

Note that you may wish to choose zero positions that best suit your method – these might not correspond to the zero positions sensed from the joints in the model.

  1. Calculate using Lagrangian Dynamics a set of equations describing the free motion of the moving parts of the gimbal axes. You of course need to include gravity in these calculations. Use Matlab’s ODE solver functions to solve these equations and compare them with the Simscape model. Inertia and the centre of mass locations will be available from the Solidworks models.
  2. Create a model of a suitable motor (some research might be required here to identify parameters) and implement with a basic PID type control scheme, in a manner similar to that outlined in the tutorial material. In the actual gimbal, the camera orientation can be sensed using an IMU or similar, which can give angular position and derivatives, as well as linear accelerations. Locking two of the three axes, try to maintain a constant orientation about the third while rotating the base irregularly.