This post briefly describes my journey to discovering the ultimate method for physics based dextrous object manipulation in the Unity or Unreal game engines.
In short, so far I have been unsuccessful.
There is a body of published work on this topic [1,2]. Most of the research I have come across so far do not use a purely physics based approach. However, there are a few groups out there who are coming pretty close to using purely physics based grasping [3,4].
The general idea

Image adapted from [5]
The image above, shows the general grasping principle in action, which consists of three components:
1. The users tracked hand and fingers (green cuboids), not visible to the user
2. The virtual, physics hand, visible
3. A virtual physics enabled (rigid body) object
The users tracked hand (kinematic) and physics hand interact via a set of spring-dampters, which connect each finger to their corresponding virtual counterpart and allows for the physics hand to realistically interact/collide with virtual objects in a compliant manner. In the example image above, the users hand has inter-penetrated the virtual object, but the physics hand has comformed to the object.
Although this approach results in fairly realist hand-object behaviour, it does not actually achieve stable, physics based grasping of the object. To this end, most solutions resort to some heuristic (rules) to create the illusion of physics based stable grasping, but never actually achieve it.
For a physics based grasp, the grasping and frictional forces between the virtual fingertips and the virtual object must be simulated, which is much more complicated than applying a few simple if-else statements.
Below I will post about my tested:
> Appraoches
> Results and
> Suggestions for future improvements
- A Hinge Joint approach
17th June 2020
This first attempt creates two hinge joints at the contact points between the tip of the digits and the target object.

References:
[1] Borst, C. W., & Indugula, A. P. (2005). Realistic Virtual Grasping. Proceedings of the IEEE Virtual Reality, 1–9.
[2] Nasim, K., & Kim, Y. J. (2016). Physics-based Interactive Virtual Grasping. Proceedings of HCI, 1–7.
[3] Holl, M., Oberweger, M., Arth, C., & Lepetit, V. (2018). Efficient Physics-Based Implementation for Realistic Hand-Object Interaction in Virtual Reality (pp. 175–182). Presented at the 2018 IEEE Conference on Virtual Reality and 3D User Interfaces (VR), IEEE. http://doi.org/10.1109/VR.2018.8448284
[4] Nasim, K., & Kim, Y. J. (2016). Physics-based Interactive Virtual Grasping. Proceedings of HCI, 1–7.
[5] Vershoor, M., Lobo, D., & Otabuy, M. A. (2018). Soft Hand Simulation for Smooth and Robust Natural Interaction, 1–8.