What you're looking for is doable but it is difficult for beginners. There is a plethora of skills you need. The skills are
1- Mathematical modelling: The first step for any project is to derive the mathematical model of your system. This requires expertise in specific fields. For manipulators, you need to apply, for example, Netwon's laws to derive the dynamics equations of your manipulator. Please take a look at these books. These are the most common textbooks in introduction to robotics.
- Robot Manipulators by Paul MIT Press
- Introduction to Robotics Mechanics and Control 3th by Graig
- Robot Modeling and Control by Spong and Et. al.
- A mMthematical Introduction to Robotic Manipulation by Murray and Et. al.
2- Numerical Analysis: mathematical models are usually in the form of differential or difference equations. Because these equations are highly nonlinear, the only solution is to utilize numerical methods to solve them.
3- Control Strategy: to move your robot, you need control methods so that your robot follow your commands. Linear and nonlinear techniques are common. Usually for highly nonlinear models like manipulators, you need nonlinear methods.
For linear Control books: (common textbooks in universities)
- Control Systems Engineering by Nise (highly recommended)
- Automatic Control Systems by Golnaraghi and Et. al.
- Modern Control Systems by Dorf (extremely popular but not easy for the first read)
- Modern Control Engineering by Ogata
For nonlinear Control books:
- Nonlinear Control Systems Analysis and Design by Marquez (highly recommended)
- Nonlinear Systems by Khalil (highly recommended).
4- Computer Graphics: to draw and simulate your manipulator, you need a good background in computer graphics. For purely graphics, you may need to learn OpenGL (i.e. for all OSs) or DirectX (i.e. for Windows). You could use any programming languages for this matter. For C++, there are numerous libraries for simplifying graphics such SDL2, Glue, FreeGlut, SMFL, etc. These libraries not for drawing rather they allow the interaction with hardware (e.g. mouse, keyboard) but they are simple so you can learn them very fast.