Keeping direction unchanged during spatial motion 1

The green disk lower end moves along a 3D curve. When blue disk is immobile, green plate (fixed to green disk) performs spatial motion without rotation around all three coordinate axes thanks to yellow planar and orange spatial parallelogram mechanisms. The grey cylinder is connected to the base via a spherical joint (not shown). The blue piston is connected to the green disk via a spherical joint. Pay attention to violet universal joints (2 DoF). Angular position of the green plate in horizontal plane ca