Four bar linkage forward kinematics question

[winston1234]

Hi, this is my first post on this forum.

I have a design for a machine with two mutually perpendicular revolute joints, i.e.

a base,

a hinged joint,

an arm,

a hinge perpendicular to the first joint,

second arm.Using D-H forward kinematics I've got code working using 4*4 transformation matrices.

Now, there's a proposal to change one of the revolute joints to a 4-bar linkage.
All the joints in the new linkage will be parallel to the original axis.

(ASCII art attempt:)

(+ = joint)

|
+
|
-----

becomes

--------I--------
---+__I___+
---/ ---------\
--/------------\
-+__________+
---------------------

This means the simple revolute joint must be replaced by four
offset parallel revolute joints, which form a closed loop.

The simplicity of the original arrangement meant it was quite straightforward
to do the kinematics. The proposed arrangement has me confused.

So, I _think_ I need to replace the simple 4*4 matrix describing a revolute joint,
with a matrix describing the 4-bar linkage.

The treatments I've found are too general for me to figure it out.

Can anyone out there help me? How do I derive the new matrix?
Or is there a better approach?

Winston

 

[Jhero]

Dear Winston,

Thank you for sharing your design for a machine with two mutually perpendicular revolute joints. It sounds like you have put a lot of thought and effort into developing this machine, and I'm sure it has great potential.

Regarding the proposed change to one of the revolute joints to a 4-bar linkage, I can understand why this may have you feeling confused. Changing the design of a machine can often be a complex and challenging task.

I would suggest taking a step back and first understanding the kinematics of a 4-bar linkage. This will help you better understand how the joints and links move in relation to each other. Once you have a good understanding of the kinematics, you can then work on deriving the new matrix for the 4-bar linkage.

There are many resources available online that can help you with this, such as tutorials, videos, and even simulation software. I would also recommend consulting with other engineers or scientists who have experience with 4-bar linkages for their insights and advice.

As for a better approach, it ultimately depends on your specific goals and requirements for the machine. It may be worth considering if there are alternative designs that can achieve the same or better results without the added complexity of the 4-bar linkage.

I hope this helps and wish you the best of luck with your project!