Mechanisms and linkages are complicated. To design them from scratch and understand them, you need to be able to do in-depth analyses and calculations. One of the most basic things to understand is how to use the "Chebychev–Grübler–Kutzbach criterion" or "Gruebler's Equation" to analyze the degrees of freedom of a linkage. I believe the mechanism in that video is a 6 bar linkage. Using Gruebler's equation, we can see that with 6 links, and 7 pins, we have 1 DOF to control the mechanism: 3*(6-1)-2*7-0=1
The structured roles and guidelines are the in-depth analyses that you want to avoid. You might be able to start learning from something like "Mechanisms and Mechanical Devices Sourcebook" by Neil Sclater
Mechanisms and Mechanical Devices Sourcebook, 5th Edition https://www.amazon.com/dp/0071704426/ref=cm_sw_r_cp_api_glc_fabc_oF06FbJ236V01
This covers mostly mechanism modeling. I enjoy it and find it useful for my job. I used to work at Intuitive Surgical.
reformatting because this is the answer...
Mechanisms and Mechanical Devices Sourcebook by Neil Schlater
Amazon link or a PDF
You want this.
Anyone who creates an invention is unknowingly using TRIZ:
https://en.m.wikipedia.org/wiki/TRIZ
I use this book a lot when I am really stumped:
Mechanisms and Mechanical Devices Sourcebook, 5th Edition https://www.amazon.com/dp/0071704426/ref=cm_sw_r_cp_apa_fgkyBb0873F14