Collision detection for Arrows and Melee. How to properly setup physics/collision?

For accurate collision detection with fast-moving objects like your arrows, you need to customize a bit:

 public LayerMask layerMask;
 private bool impacted = false;
 private float skinWidth  = 0.1f; //probably doesn't need to be changed 
     private float minimumExtent; 
     private float partialExtent; 
     private float sqrMinimumExtent; 
     private Vector3 previousPosition; 
     private Rigidbody myRigidbody;
 
     private Vector3 lastPosition;
 
 void Awake() { 
         myRigidbody = GetComponent<Rigidbody>();
         previousPosition = myRigidbody.position; 
         minimumExtent = Mathf.Min(Mathf.Min(GetComponent<Collider>().bounds.extents.x, GetComponent<Collider>().bounds.extents.y), GetComponent<Collider>().bounds.extents.z); 
         partialExtent = minimumExtent * (1.0f - skinWidth); 
         sqrMinimumExtent = minimumExtent * minimumExtent; 
 
     }
 
 
 void FixedUpdate() {
         
 
             Vector3 direction = transform.position - lastPosition;
             Ray ray = new Ray(lastPosition, direction);
             RaycastHit hit = new RaycastHit();
             if (Physics.Raycast(ray, out hit, direction.magnitude, layerMask))    {
                 Impact(hit.point, hit.normal, hit.collider.gameObject);
             }
             
             this.lastPosition = transform.position;
         }
     }
 
 void OnCollisionEnter(Collision collision) {
         
         if(impacted == true) {
             return;
         }
         Impact(collision.contacts[0].point, collision.contacts[0].normal, collision.collider.gameObject);
         impacted = true;
     }

 void Impact(Vector3 pos, Vector3 normal, GameObject hitObject) {
                 //Apply damage to the hit gameObject, or whatever
         Destroy(gameObject);
     }
     

Kinematic rigidbodies indeed don't reigster collisions. If you want to make a rigidbody register a collision with another collider without making it react to physics, set the other collider to be IsTrigger = true. You can also use things like SphereCastAll to hit multiple enemies in front of you when you swing your sword, or just check if there's actually one.

Hey there, this works flawless for me (pretty simple but effective):

Actually i'm sending a ray from the arrows position to its forward vector to check if he hits something. However you should only use that code for a skyrim like archery system (sending the ray costs some performance).

 using UnityEngine;
 
 public class Arrow : MonoBehaviour {
 
     public Transform tipTransform;

     public GameObject _explosionEffect;
 
     private AudioSource _audioSource;
     private Rigidbody _rb;    
 
     private void Awake() {
         _rb = GetComponent<Rigidbody>();
         _audioSource = GetComponent<AudioSource>();

         // Set the center of mass to the arrows tip to make the arrow flight realistic
         _rb.centerOfMass = tipTransform.localPosition;
 
         Destroy(gameObject, 5f); // Make sure arrow gets always destroyed
     }
 
     private void FixedUpdate() {
         RaycastHit hit;

         // Send raycast from arrows position to is forward vector to detect if something gets hit
         if(Physics.Raycast(_rb.position, _rb.transform.forward, out hit, 2f))
             Explosion(hit.collider, hit.point);
     }
 
     private void Explosion(Collider other, Vector3 point) {
         Debug.Log("Arrow hitted: " + other.transform.name);
 
         // Spawn an explosion effect
         Destroy(Instantiate(_explosionEffect, point, Quaternion.identity), 2f);
 
         Destroy(gameObject);
     }
 }

Greets

This might help http://docs.unity3d.com/Manual/CollidersOverview.html