Does Robot Axis arrow affect in final output?

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Over here all the links arrows Red, Blue, and Green are pointing in different directions on the other side in Kuka experimental official library is pointing towards the same direction except the tool point.

I believe you created this robot support package yourself, is that correct?

If so: the reason the links in the robot support packages of ros-industrial/kuka_experimental are all oriented the same is because of REP 103: Standard Units of Measure and Coordinate Conventions. In a nutshell: standard frame orientation is: X+ 'forward', Y+ 'to the left', Z+ 'up' (right-handed system).

By using that same convention in the *_macro.xacros in robot support packages, transforms between frames in the same chain, and from objects in the environment to those frames do not result in unexpected rotations. Additionally, adhering to conventions is a good idea, as it will make your own artefacts much easier to reuse by others, who will also be expecting REP 103 compliance.

if I give my robot simulator to go in a particular x,y,z position the same trajectory will be followed by my real robot? Or due to this issue, my robot may mislead and end up with different results?

if by "trajectory" you mean a list of Cartesian poses, then in typical industrial robot use-cases you only define the pose of the Tool Centre-Point, not of any of the intermediate links (typical industrial robots don't give you any direct control over the intermediate links in any case). So as long as you've made sure that whatever you use for TCP frame in your ROS application corresponds to what your real robot has, things should-just-work.

But this all depends on what the parent is of the transform to your TCP frame. If you're using base_link->my_tcp and base_link is not in the correct location wrt your real hw, things will-not-just-work.