In this tutorial you create a slider crank mechanism using a combination of revolute and
cylindrical joints. You will also experiment with additional plotting utilities in CATIA.
1 Problem Statement
A slider crank mechanism, sometimes referred to as a three-bar-linkage, can be thought
of as a four bar linkage where one of the links is made infinite in length. The piston based
internal combustion is based off of this mechanism. The analytical solution to the
kinematics of a slider crank can be found in elementary dynamics textbooks.
In this tutorial, we aim to simulate the slider crank mechanism shown below for constant
crank rotation and to generate plots of some of the results, including position, velocity,
and acceleration of the slider. The mechanism is constructed by assembling four parts as
described later in the tutorial. In CATIA, the number and type of mechanism joints will
be determined by the nature of the assembly constraints applied. There are several valid
combinations of joints which would produce a kinematically correct simulation of the
slider crank mechanism. The most intuitive combination would be three revolute joints
and a prismatic joint. From a degrees of freedom standpoint, using three revolute joints
and a prismatic joint redundantly constrains the system, although the redundancy does
not create a problem unless it is geometrically infeasible, in this tutorial we will choose
an alternate combination of joints both to illustrate cylindrical joints and to illustrate that
any set of joint which removes the appropriate degrees of freedom while providing the
capability to drive the desired motions can be applied. In the approach suggested by this
tutorial, the assembly constraints will be applied in such a way that two revolute joints
and two cylindrical joints are created reducing the degrees of freedom are reduced to one.
This remaining degree of freedom is then removed by declaring the crank joint (one of
the cylindrical joints in our approach) as being angle driven. An exercise left to the
reader is to create the same mechanism using three revolute joints and one prismatic joint
or some other suitable combination of joints. We will use the Multiplot feature available in CATIA is used to create plots of the simulation results where the abscissa is not necessarily the time variable.
Slider Crank Mechanism 4-3
2 Overview of this Tutorial In this tutorial you will:
1. Model the four CATIA parts required.
2. Create an assembly (CATIA Product) containing the parts.
3. Constrain the assembly in such a way that only one degree of freedom is unconstrained. This remaining degree of freedom can be thought of as rotation of the crank.
4. Enter the Digital Mockup workbench and convert the assembly constraints into two revolute and two cylindrical joints.
5. Simulate the relative motion of the arm base without consideration to time (in other words, without implementing the time based angular velocity given in the problem statement).
6. Add a formula to implement the time based kinematics associated with constant
angular velocity of the crank.
7. Simulate the desired constant angular velocity motion and generate plots of the kinematic results.
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