Cars and Automotive Design

You can design a suspension geometry in MSC ADAMS software , MATLAB SIMULINK, but the easiest of them all is to design in LOTUS software. Lotus is not designed for it but you can do various iterations to get the result but before that you have to study the suspension geometry. some books i can refer are vehicle dynamics books from carrol smith and another is from Reza zazar.

You can do it without using software, I would recommend books by Allan Staniforth and 750 racer by Peter Herbert & Dick Harvey if you can get your hands on them. Otherwise watch https://www.youtube.com/watch?v=VbReLNi2JP4 to get an understanding of the geometry and what you want to achieve. Once you understand what you want to achieve you can use any 3d software.

I'm not a suspension expert at all, but I've been using various CAD programs for over a decade. I agree with previous posters that you should first understand the the theoretical fundamentals of suspension design before getting into CAD. But once you do, I see no reason not to use Fusion360 by Autodesk. You can obtain a free hobbyist or student license and essentially get a full blown parametric solid modeling CAD program with joint, motion, interference & analysis capabilities. Go for it! All the best!

Very good video ;-)