Coupler Curve and Coupler Point Mechanism Synthesis

Four-Bar-Definition

A four-bar mechanism, indicated to the left by [AoABBo], is a closed kinematic chain consisting of 4 links. One of the links is the fixed link [AoBo]. The opposite link, is the coupler [AB]. It is the base of a coupler-triangle [ABK], the vertex of which, the coupler-point K, describes the coupler-curve when the mechanism is moved.

It is often of engineering importance to synthesise a four-bar mechanism that:

Guides a coupler point to give a particular coupler curve, or shape

- or -

Guides a coupler point between a number of points

MechDesigner for Coupler Curve Synthesis

The equation of a coupler-curve is of the sixth degree and its properties are 'tricircular sextic'. We do not need to know how to solve this equation.

There are three other ways that MechDesigner can help you find coupler-curves to suit a particular application.

tog_minus        Coupler Curve: Trace-Points and Design Set

Option 1: Summary of Steps

Drag a point in the Mechanism graphic-area and watch a Coupler Curve update in real time. This is easy to do.

1.Open the Part-Editor to add a Point to the coupler of a mechanism with the Add Point tool

Do not add dimensions or constraints to the Point.

2.Close the Part-Editor
3.Add a Trace-Point to the Point
4.Drag and drop the Point in the Mechanism-Editor

Option 2: Summary of Steps [see more details below].

Add an atlas or structured array of Points to a coupler in a mechanism.

Watch the complete atlas of coupler curves update as you edit the mechanism

1.Assemble a Four-Bar Mechanism

You can make it a Crank-Rocker or a Crank-Slider.

2.Add a number of Lines to the Coupler to give an array of Points.

It is useful to add constraints to the Lines. For example, to make the Lines equal in length, vertical (relative to the Coupler)

You can also make the Lines proportional to the length of the Coupler, or a fraction of the Coupler.

3.Add a Trace-Point to the Point at the end of each Line.
4.Add a Design-Set so you can edit the lengths of the Parts and the Lines in of the array. If you make the length of each Line equal, then the Design-Set needs only one dimension, other than the length of each Line.

Option 2: More Details

Atlas1

A Crank-Rocker

We are trying to find the shape of a coupler curve not the absolute size it.

When we find the shape of the coupler curve, we can scale all the Parts to suit the actual size we need.


Therefore, the length of the frame can be fixed.

In this example, I have made it 100mm.

 

Atlas5b

A Crank-Slider

 

Make the length of the Frame fixed.

In this example I have made it 100mm long.

Atlas2

Add a number of Lines to the coupler to make an array of Points.

We will add Trace-Points to each Point at the ends of each Line, to give a number of coupler-curves.

I have found it best to not add too many lines. In this example,

There are eight pairs of lines, mirrored about the axis of the coupler [AB]
The Lines are equal length, vertical, and equally spaced along the axis of the coupler.
The space between each Line is a fixed ratio of the length of the coupler. In this case, the space is equal to half the length of the coupler.
There is one dimension that gives the length of the coupler.
There is a different dimension that gives the length of one Line. All of the other Lines are made an equal length.

Atlas3

Hide the Elements that you do not need to see

In this example, I have hidden all the elements to show only the Points.

You can also make the Points smaller with the Symbol size parameter in the Accessibility Settings

Atlas4a

Crank-Rocker Mechanism - Add Trace-Points to each Point in the array

This image shows the mechanism is reduced to four CAD-Lines.

When you hide the Part-Outlines, you can see the Trace-Points, or Coupler Curves, more clearly.

Atlas5a

Crank-Slider Mechanism - Add Trace-Points to each Point of the Atlas of Points

This image shows the mechanism is reduce to four CAD-Lines, and the coupler curves are shown.

Atlas5

Add a Design-Set

In the Design-Set:

Add the Length of Each Part - excluding the Frame as this is fixed
Add the dimension that gives the offset of the Points from the Coupler
Edit the Dimensions while the mechanism is cycling or not-cycling.

 

Watch the Coupler Curves change as you edit a dimension in the Design-Set

This is the Crank-Rocker Mechanism.

A Design-Set is used to adjust the Part lengths and the offset of the Coupler Curve from the Coupler.

 

Watch the Coupler Curve Change as you edit the Dimensions

This is the Crank-Slider Mechanism.

A Design-Set is used to adjust the Part lengths and the offset of the Coupler Curve from the Coupler.

tog_minus        Coupler Points: Constraint-Base Sketch Editor

Summary of Steps

1.Add Precision Points* to the Base-Part for which we would like a Coupler Curve to move through.

These are the Points we would like the Coupler to pass through.

2.Add the three (or four or five) lines, that are equal in length, to represent the Crank, Coupler, Rocker.
3.Make the Points that are at the end of the Lines that represent the Crank and Rocker, and would normally be fixed to the machine frame, to be coincident.

Even though they would normally be fixed to the machine frame, we leave these Points floating during the synthesis.

4.Add two further lines to the Couplers to make triangles. Add equal constraints to the sides of the triangles, so that the triangles are congruent.
5.Add Coincident Constraints between the apex of each triangle to one Precision Point.

* They are 'Precision Points' because the point on the coupler move through them, exactly.

CouplerPoint Synthesis-3Points

Add the Points

Edit the Base-Part

Add the Precision Points

CouplerPoint Synthesis-3Points-2

Add Lines to represent the Mechanism at the First Coupler Precision Point

A line for the Crank, the Coupler and the Rocker.

Add two lines to the Coupler to create a triangle.

Make the apex of the triangle coincident with one of the Precision Points.

Do NOT dimension or fix the points that will identify the grounded Points.


The 'Crank' and the 'Rocker' are inter-changeable at this stage. We do not know which will be which.

CouplerPoint Synthesis-3Points-3

Add a second set of Lines to represent a different Mechanism at the Second Coupler Precision Point

The lines for the Crank and Rocker at the second position should join the ends of the first Lines that represent the first Crank and Rocker.

Add two lines to the Coupler and make the apex of the triangle coincident with different Precision Points

Use the Equal Constraint tool to make the 'links' equal in length and the two sides of the triangle on the coupler equal in lengths so that the triangles are congruent.

Do not fix the grounded joints to the frame. Leave them 'floating' so that MechDesigner find the best result.

CouplerPoint Synthesis-3Points-4

Add a second set of Lines to represent a different Mechanism at the Second Coupler Precision Point

Make the corresponding links the Equal in Length as for the other Coupler Precision Points

You will likely need to drag the 'fixed' Points that are potentially the actual fixed Points of the four-bar Linkage.

Be aware that the congruent triangle may 'invert' about the Coupler. You must fix this so that the triangles remain congruent.

Continue for the Forth and Fifth Coupler Precision Points

If you add more, it is very likely that the model will have very long link lengths unless you happen to be lucky.

You will need to drag the 'fixed' Points that are potentially the actual fixed Points of the four-bar Linkage.

CouplerPoint Synthesis-3Points-5

Close the Part-Editor and construct the Mechanism.

1.Use the Measurement FB to confirm the lengths of the Lines,
2.Make the Parts the same length as the Measurements
3.Add a sketch in the Coupler to give a Point that is coincident with the Precision Coupler Points

I have added a sketch-loop and Profile.

4.Add a Motion-Dimension FB. Select a line in the Base-Part so that the Mechanism coincides with one of the Precision Points when the Base Value of the Motion-Dimension FB is zero

 

Add the Motion and Cycle the Mechanism

1.Add a Motion FB
2.Edit the motion so that it rotates the 'Crank' an angle equal to the change in angle of the lines at the Motion-Dimension FB.
3.Cycle the Mechanism.

The video shows the mechanism cycling.

tog_minus        Instantaneous Kinematics

Instantaneous Kinematics gives particular properties of a Coupler Curve at particular instants.

I have prepared a different topic on IK - See About Instantaneous Kinematics.

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