Two, Three, Four and Five Position Synthesis

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Two, Three, Four and Five Position Synthesis

Two, Three, Four and Five Position Synthesis

It is often of engineering importance to design (synthesize) a four-bar mechanism that guides a machine component, often a tool or end-effector, through a number of positions.

When the machine component is the coupler of a four-bar, the synthesis is frequently called Position Synthesis.

It is possible to find the positions of the coupler with a drawing board and with mathematics. Wee can also obtain wonderful insights of the design process when we use Constraint-Based Sketch Tools, especially when we want to find four or five separate positions. Also, the tools give us insights of Circle Point Curves (Cubic of Stationary Curvature), center Point Curves, Burmester Points.

Definition of Position Synthesis:

Position Synthesis is 'find a mechanism to move a machine component through different, defined positions, relative to a different machine component.

We need a coordinate system to define the different positions. Luckily, Parts and Lines in MechDesigner have Coordinate Systems.

Part's Coordinate System: Origin is its start-Point' X-axis is along its CAD-Line towards its end-Point.

Line's Coordinate System: Origin is its start-Point; X-axis is along it towards the end-Point.

Thus, we can use Lines in the Part-Editor in the same way as we use Parts in the Mechanism-Editor.

We use geometric constraints in the Part-Editor and Joints in the Mechanism-Editor.

This is because:

Coincident-Constraint between two Points is exactly the same as the Pin-Joint.

Coincident-Constraint between two Lines is exactly the same as the Slide-Joint.

Parts and Lines have an 'Origin' and 'X-axis' direction. Therefore, we can represent a 'Plane' and its Position with a Part in the Mechanism-Editor and a Line in the Part-Editor.

What is the Design Statement of Position Synthesis?

Design Input:

Guide a Plane or Part through a number of specified positions.

Design Output:

A four-bar mechanism that guides its coupler through each specified position.

MechDesigner for Position Synthesis

Two and Three Position Synthesis:

We can do the synthesis for two and three position synthesis in three ways:

Procedure 1: Uses traditional graphical techniques ('use a compass to draw arcs, perpendicular bisectors, intersections...')

Procedure 2: Uses 'traditional graphical techniques' and also simple constraints for the arcs and lines.

Procedure 3: Uses only the Constraint-Based Sketch Tools

There is an example of each method in the Three-Position Synthesis.

Four and Five Position Synthesis:

Procedure 4: Uses more Advanced use of the Constraint-Based Sketch Tools

Rather than find a solution for cubic curves, we use the powerful Constraint-Based Sketch Tools in the Part-Editor to find two Points in the coupler Part that move around the circumference of a circle.

Note: It is not easy to find a solution for five different positions. Small changes to the Plane Positions can give kinematic results that are amazingly different.

You might need to experiment with the four and five position synthesis for a long time to get a satisfactory result.

tog_minusTwo Position Synthesis
tog_minusThree Position Synthesis
tog_minusFour Position Synthesis
tog_minusFive Position Synthesis - not complete, images only.

tog_minusFive Position Synthesis - not complete, images only.