The equations modeled here are for a four-bar linkage with pinned revolute
joints. This is a one-DOF system and is defined by an input angle θ _{2}.
The necessary kinematics for the four-bar linkage can be found from the
angular position, velocity and acceleration. A web applet of this model
can be found here.Kinematics are taken from the textbook ## PositionThe angles can be found by solving a vector loop equation, which is written in terms of exponentials for simplicity:Solving the vector loop equation in terms of θ2, where θ1=0, gives trigonometric relations for the remaining angles: The expressions are simplified by collecting similar terms, which are given in the following relations:
It is important to note that the arctangent function has singular points and is often numerically implemented only over -pi/2 to pi/2. Adequate evaluation may require interjecting numerical noise to avoid the singularities if using previously implemented methods. ## VelocityIn a similar fashion angular velocity for the driven angles can be found by solving the vector velocity loop equation:The driven angular velocities are then given below in terms of the angles, which must be solved using the equations from above. ## AccelerationFinally, the angular acceleration of the driven angles can be solved for using the solutions to the angular position and velocity from the previous equations and the vector acceleration loop equation:The angular accelerations are given below in terms of simplified variables: The simplified terms used in the equations above are given below: |

Miscellaneous >