kinematics-of-multi-body-system

Implementation of a general planar mechanism kinematics analysis tool using absolute coordinates in MATLAB.

Usage

To use this project, the mechanism must be defined in a specified way as demonstrated in the example below. The full detail of the example mechanism can be found in the directory /src/preprocessor.

To define the mechanism, a MATLAB struct is used. The definition follows the pattern: mechanismName.bodyName.bodyProperties

bodyProperty includes:

• the location of its center of mass,
• joints that are associated with the body and their properties which include:
  • Joint location (if the type is P, the location can be just [NaN, NaN]')
  • Joint type either P for translational or R for revolute
  • Logical variable driving to indicate if there is a driving constraint associated with the joint
  • If driving is true, specify the motion as an anonymous function of time, fAB
  • Special Case: if the joint is translational and if it is directly connected to the ground, a reference point must be provided to define the axis of translation accurately.
• Initial values of the kinematic variable (position q0, velocity dq, and acceleration ddq)
• Marker points for which kinematic analysis is to be performed
  • Marker points on a body named bodyName is defined as: bodyName.markers.markerName.Location. Then assign the location.

Example

Mechanism and assignement of absolute coordinates (it doesn't matter where the coordinates are assigned on the bodies; however, for convenience they are put at each CoM):

Coordinates of bodies CoM and joints:

Example of defining mechanism and its ground

mechanism = struct();
% Ground: center of mass and initial values of the kinematic variables
% These are fixed since the ground doesn't move.
mechanism.ground.com = [0, 0]';
mechanism.ground.q0 = [0, 0, 0]';
mechanism.ground.dq = [0, 0, 0]';
mechanism.ground.ddq = [0, 0, 0]';

Example of defining a body:

% Plate C3: center of mass and initial values
mechanism.bodyC3.com = [0.15, 0.45]';
mechanism.bodyC3.q0 = [0.15, 0.45, 0]';
mechanism.bodyC3.dq = [0, 0, 0]';
mechanism.bodyC3.ddq = [0, 0, 0]';

Example of defining a joint without driving:

mechanism.bodyC3.joints.joint_D.type = 'R';
mechanism.bodyC3.joints.joint_D.location = [0.2, 0.6]';
mechanism.bodyC3.joints.joint_D.driving = false;

Example of defining a joint with driving:

mechanism.bodyC3.joints.joint_AD.type = 'P';
mechanism.bodyC3.joints.joint_AD.location = [NaN, NaN]';
mechanism.bodyC3.joints.joint_AD.driving = true;
mechanism.bodyC3.joints.joint_AD.fAB = @(t) -0.1*sin(1.5*t+0);  % Specify motion

Special Case: Defining translational joint on the ground:

mechanism.ground.joints.jointD.type = 'P';
mechanism.ground.joints.jointD.location = [NaN, NaN]';
mechanism.ground.joints.jointD.driving = false;
% Put a reference for defining the translational axis
mechanism.ground.joints.jointD.reference = [5, 4]';

Example of defining a marker point on a body

% Markers associated with bodyC3
mechanism.bodyC3.markers.D.location = [0.2, 0.6]';

Performing analysis

• Add files to the MATLAB PATH

% Initialize the system by adding all files to the MATLAB PATH
Initialize;

• get the mechanism definition

% Get the mechanism for which kinematics analysis is to be performed
mechanism = defineMechanism;

• Perform kinematic analysis for bodies of the mechanism

%% Kinematics analysis
% solve the kinematic problem for the mechanism bodies and their marker
% points.
endTime = 5;
steps = 100;
kinematics = Kinematics(mechanism, endTime, steps);

Visualization

To visualize bodies kinematics analysis result specify the option 'b' or 'B' for markers specify option 'm' or 'M'. This will generate a plot of position, velocity and acceleration of each specified body/markers in the mechanism respectively.

%% Visualization
% To generate plot of kinematics result analysis for the entire 
% bodies or markers in the mechanism use: 

% Visualizer(markersKinematics, 'b')
% Visualizer(markersKinematics, 'm')

% Or we can specify the body name of interest
bodyNames = {'bodyC1', 'bodyC10'};
Visualizer(kinematics, 'b', bodyNames)

% The same thing for markers as well
bodyNames = {'bodyC8'};
markerNames = {'K', 'I'};
Visualizer(kinematics, 'm', bodyNames, markerNames)

• Bodies Kinematics:

• Marker Points Kinematics: