Is the Normal Spherical Image of a Curve Always Non-Constant?

[drc4rd1n]

Helo..i have a problem about geometry..
How to show that the normal spherical image of x is never constant?

 

[rahuliitkgp]

what is normal image of a point??
please explain

 

[drc4rd1n]

what is normal image of a point??
please explain

all functions anda curves considered here are assumed to be of class at least C³.
If x(s) is a regular curve parametrized by arc length s, then t:(a,b)-> R³ defined a curve on S²..

this curve might not be regular and is called the tangent spherical image of x.
the normal spherical image n(s) and binomial spherical image b(s) of x can also be defined.

so, the question is how to proof that the normal spherical image of x is never constant?