Four-bar Kinematic-Chains

Four-Part Kinematic-chains - which you may call 'four-bar mechanism', 'four-bar linkage', or even 'four-bar' - are the basis of the most frequently used mechanism in packaging machines.

This tutorial uses Pin-Joint and Slide-Joint elements. We combine the joints in different ways to configure the mechanism in different ways.

Objective of this Tutorial

To build kinematic-chains that have a total of four Parts and four Joints.
To learn about Dyads.


If the lengths of the Parts and kinematic-chains in the images and videos below are different to your model, then I have edited their lengths to show a kinematic configuration.

Please edit the length of the Parts to be the same approximate length as the Parts in the images when they are clearly different to your model. To edit the length of a Part, see Step 1.7: Edit the Length of the Crank.

Terminology: Reminder from Tutorial 1

Elements :

Elements are the objects we add to the model. They represent the objects in a machine.

Nearly always: the sequence of steps we use:

1. Add the element... the element's dialog-box...
3....edit the element's parameters in the element's dialog-box.

In addition to elements that you can see in the graphic-area [Parts, Pin-Joints, ...], there are elements you cannot see [Constraints, ...]

Plane :

the flat surface that is at a precise angle and position relative to the XYZ axes and XYZ coordinates. When we add a Mechanism-Editor to a Plane, and that editor is active, then the 'Front-View' looks directly at the Mechanism-Plane.

Mechanism-Editor :

the workspace that includes the Mechanism-Plane , the graphic-area, the contextual -toolbars, and the Mechanism-Editor name-tab.

Part :

an element that becomes the moving, or fixed, rigid-bodies in the machine.

Joint :

Kinematic-Joints constrain the relative movement between two Parts.

Pin-Joint :

a Kinematic-Joint that constrains together two Points, with one Point in two different Parts.

Kinematic-Chain :

two or more Parts joined together with one or more Joints.

Kinematically-Defined :

Part or Kinematic-Chain that moves in a manner as specified by at least one Motion-Part. Parts that are kinematically-defined have Green Part-Outlines.

When a Part has a:

Green Part-Outline: the Part is a kinematically-defined Part. We also call it a 'Solved Part'.
Blue Part-Outline: the Part is not a kinematically-defined Part. We also call it an 'Unsolved Part'.

Our target is to make sure we have Green Part-Outlines, ALWAYS.

Motion-Part :

a Part, that is kinematically-defined, whose motion is precisely specified with a Motion-Dimension FB

Motion-Dimension FB :

a Function-Block[FB] that specifies the angular or linear position, velocity and acceleration of a Part as a function of the Master-Machine-Angle [there are exceptions]

Linear-Motion FB :

a Function-Block[FB] whose output is 0 – 360 [default]. You can edit the initial value parameter to delay or advance the timing of a kinematic-chain.

Gearing FB :

a Function-Block[FB] with which you can apply parameters to the input motion-values in the form of a linear equation to give a different output.

Master-Machine-Angle :

the 'clock' that, when you cycle the machine, moves at a constant rate from 0 to 360, again and a again.

The positions of all kinematically-defined Parts are a function of Master-Machine-Angle. The Master-Machine-Angle [MMA] 'beats the drum' of the machine.

Rocker :

a Motion-Part that rotates with a specific motion relative to a different Part. It may index progressively, rotate continuously [as a Crank], or oscillate back-and-forth.

Terminology: Tutorial 2

Slide-Joint :

a Kinematic-Joint that constrains together two Lines, with one Line in two different Parts.

Slider :

a Motion-Part that slides with a specific motion relative to a different Part. It may index progressively, slide continuously [as a 'conveyor'], or oscillate back-and-forth.

Dyad :

a Dyad is a kinematic construction of:

2 Parts
3 Joints

Each of the two Parts in the Dyad is joined to two different Parts and then they are joined together, to make three Joints in total.

Dyad Closure :

a different way to assemble the same Dyad.

Motion FB :

a Function-Block[FB] that links a Motion-name and motion-values in MotionDesigner to a kinematic-chain.

Crank-Rocker :

a kinematic-chain with one Motion-Part [the Crank] and one Dyad that has three Pin-Joints, and the output oscillate ['rocking'] back-and-forth.

Crank-Slider :

a kinematic-chain with one Motion-Part [the Crank] and one Dyad that has two Pin-Joint and one Sliding-Joint, with the output reciprocating ['sliding'] back and forth.

Mechanism names :

Scotch-Yoke, Whitworth Quick-Return are common names for some 'standard' mechanisms you may come across at different times in a machine.


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Tutorial and Reference Help Files for MechDesigner and MotionDesigner 13.2 + © Machine, Mechanism, Motion and Cam Design Software by PSMotion Ltd