You can simulate the forward kinematics of an analytic 2R__P__R-PR robot downloading the following Java applet (you may need the latest version of Java):

This analytic 2R__P__R-PR robot can execute nonsingular transitions by encircling quadruple solutions of the forward kinematic problem.

For further information, see the following publications:

**Peidro A., Marin J.M., Gil A., and Reinoso O. (2015). Performing nonsingular transitions between assembly modes in analytic parallel manipulators by enclosing quadruple solutions.***ASME Journal of Mechanical Design*, Vol. 137(12), p. 122302. DOI: 10.1115/1.4031653-
**Peidro A., Reinoso O., Gil A., Marin J.M., and Paya L. (2016). A simulation tool to study the kinematics and control of 2RPR-PR parallel robots.***Proceedings of the 11th IFAC Symposium on Advances in Control Education.*

You can see the 2R__P__R-PR robot performing nonsingular transitions in the following video:

The analytic 3R__P__R robot with flat base and platform (also known as the planar Stewart platform) can also perform nonsingular transitions in a similar way: