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OpenGL OpenGL Robot Movements: combining vertical and horizontal moves into one

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I have made a robot arm for an iphone app using OpenGl.

Its forearm can turn left and right by rotating around the arm; and can also go up and down by rotating around a normal vector to its main axis.

The left/right movements are going smoothly with GlRotate; the up and down as well.
The problem comes when i would like the forearm to go the right/left at the same time as going as up and left.

The final result is the right one meaning it arrives at the final position ; however it proceeds by sequence; for example it execute the 1st GLRotate to go right; and then the 2nd Glrotate to go up.

The result i would like to see is in fact a combination of both up and right; in other words that it appears as one movement.

What are your suggestions to arrive to such result ?
Note that the axises of rotations are different for the left/right move and up/down.

Many thanks in advance for any pointers, helps you can provide :)


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