Forward-Kinematics, Inverse-Kinematics, 'Installed-Kinematics' (Tolerance Analysis)

Kinematics and Robots

Inverse-Kinematics-Robots-3

The image to the left is a typical layout that might be used to explain Forward-Kinematics and Inverse-Kinematics, when applied to Robotics.

The robot has a tool at the end of its arms. In the image it is at Point 'P'.

The Point is located in three coordinate systems.

Part Coordinate System, PCS, by coordinate xPCS, yPCS,
Machine Coordinate Systems, MCS, XMCS,YMCS
Arm Coordinate System, ACS, θACS,θACS

Transformation, in the contextual of kinematics, is the calculation needed to identify the position of a Point in different coordinate systems. You 'Transform' the Point from one coordinate system to another. There are two kinematics problems:

The 'forward kinematic' problem, which finds the position of the Tool-Point, from specified Arm-Coordinates.
The 'inverse kinematic' problem, which finds the Arm-Coordinates from a specified Tool-Point.

The transformation equations depend on the arrangement of the Joints and Parts. When you have a specific robot design, the transformation equations do not change.

Luckily, modern servo-controllers for robots have the transformation equations built in to the controller.

Terminology

Powered-Part: the Part moved by the Power Source In this case, the Power-Part is the Cam-Source is the Cam and the Power-Part is the Cam-Follower.
Tool-Part: the Part that interacts with the product or packaging.
Transforming-Dyad(s): a Dyad, or Dyads, that transform the motion from the Power-Part to the Tool-Part, or vice-versa.
Motion-Part: the Part you move with a specified motion. The Power-Part or the Tool-Part.

Forward and Inverse-Kinematics Cam Design.

When there is a dyad 'between' the Cam-Follower and the Tool, then you can use Forward or Inverse-Kinematics as your design option:

If you assign the motions to the Tool-Part, and you need to find the motion for the Cam-Follower, then it is usually called Inverse-Kinematics.
If you assign the motion to the Cam-Follower, and you need to find the motion for the Tool-Part, then it is usually called Forward-Kinematics.

 

Part with Motion-Dimension

Motion found by MechDesigner.

Forward-Kinematics

Cam-Follower

Tool-Part

Inverse-Kinematics

Tool-Part

Cam-Follower

In MechDesigner, it is easy to use Forward or Inverse-Kinematics as your design options.

MechDesigner will find the motion of all the Part in a kinematically-defined chain

However, we strongly recommend Inverse-Kinematics as the design approach.

It is much easier to edit and find the design solution. Most cam-design software uses the Forward-Kinematics approach.

Tolerance Analysis, Design Sensitivity

As an option, you can also use MechDesigner to complete a tolerance analysis, or 'dimension-sensitivity' analysis.

You can use a Magnetic-Joint and a Point-Cloud and the finished cam. You will see the motion of the Tool-Part change as you make small changes to dimensions. This is equivalent to Tolerance Analysis.

Examples of Forward, Inverse and Installation Kinematics

 

Forward Kineamatics

 

Forward Kinematics

If you design and add the motion-dimension to the Power-Part, and use a dyad to transfer the motion to the Tool-Part, then the design approach is 'Forward-Kinematics'.

In the image:

The Motion is given to the Power-Part - which happens to be the Cam-Follower Part
An RRP Dyad transforms the motion to the Tool-Part - that slides vertically.

 

Inverse Kineamatics

 

Inverse-Kinematics

If you design and apply the motion to the Tool-Part, and use a dyad to transfer the motion to the Power-Part, then the design uses 'Inverse-Kinematics'.

In the image:

The Motion is given to the Tool-Part - which slides vertically.
An RRR Dyad transforms the motion to the Power-Part, which is the Cam-Follower Part.

 

Tolerance Analysis / Installation Kinematics

Tolerance Analysis and Design Sensitivity

Whether you use the Inverse or Forward-Kinematics to design your machine, you will end up with a Cam!

There are always differences between the model and the installed machine.

It is possible to review how the differences between the model and the installed machine might affect the motion of the Tool-Part.

If you use a Magnetic-Joint to keep the Cam-Follower Roller on the Cam, then you can see how the Tool-Part change its position and motion as you edit the position of the machine centres, lengths of Parts and position and size of the Cam-Follower Roller.

You can analyse the errors between your planned motion and the actual motion, if you edit the parts by the tolerances in your detailed drawings.

You can also see which tolerances affect the tool motion more than others.

Help Files for MechDesigner and MotionDesigner 11.1 + © Machine, Mechanism, Motion and Cam Design Software by PSMotion Ltd