
starr
rigid
Immobile, stiff, and not flexible.
Nach dem langen Sitzen fühlten sich seine Glieder ganz starr an.
After sitting for so long, his limbs felt completely rigid.
rigid / fixed
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rigid
Immobile, stiff, and not flexible.
Nach dem langen Sitzen fühlten sich seine Glieder ganz starr an.
After sitting for so long, his limbs felt completely rigid.

fixed
Focused on one point and without movement, especially of eyes or a gaze.
Er blickte mit starren Augen auf die Unfallstelle.
He looked at the accident scene with fixed eyes.

rigid
In a figurative sense: inflexible, dogmatic, and holding on to fixed rules or opinions.
Seine starre Haltung in der Verhandlung machte eine Einigung unmöglich.
His rigid position in the negotiation made an agreement impossible.

stiff
Stiff and numb because of cold.
Ohne Handschuhe waren meine Finger bald starr vor Kälte.
Without gloves, my fingers soon became stiff from the cold.
The adjective 'starr' (rigid/fixed) is closely related to the verb 'erstarren' (to freeze/stiffen). 'Erstarren' means to become stiff or immobile, which explains the basic meaning of 'starr' very well.
Als er die schreckliche Nachricht hörte, erstarrte er.
When he heard the terrible news, he froze.
In the meaning 'fixiert' (fixed), 'starr' is very often combined with verbs of seeing. Typical phrases are 'starr blicken' (to stare fixedly), 'starr schauen' (to stare fixedly), or 'jemanden starr ansehen' (to stare fixedly at someone).
Die Katze schaute starr auf den Vogel im Baum.
The cat stared fixedly at the bird in the tree.
To express the cause of the stiffness, the preposition 'vor' with the dative is often used. The most common combinations are 'starr vor Kälte' (stiff from cold) and 'starr vor Schreck' (frozen with fright).
Nach dem Sturz ins kalte Wasser war er starr vor Kälte.
After falling into the cold water, he was stiff from the cold.
You can recognize the figurative meaning by the fact that 'starr' does not refer to a body or body part, but to abstract concepts. Examples are 'starre Regeln' (rigid rules), 'ein starrer Plan' (a rigid plan), or 'eine starre Meinung' (a rigid opinion).
Das Unternehmen leidet unter seinen starren Hierarchien.
The company suffers from its rigid hierarchies.
fixed / determined
For a procedure, festgelegt means that its rules have been bindingly determined. Starr evaluates the same procedure as inflexible and emphasizes that it can hardly be adapted to new situations. A festgelegter procedure is therefore not necessarily starr.

Der Ablauf der Prüfung ist so starr, dass keine Pause verschoben werden kann.
The exam procedure is so rigid that no break can be rescheduled.
Der Ablauf der Prüfung ist verbindlich festgelegt.
The exam procedure is bindingly fixed.