Sure, I can help you with that!

Vue.js Router is a powerful tool for managing routes in your application. However, one common problem you may encounter is the lack of smooth transitions when navigating between routes. This happens because Vue.js Router doesn't automatically apply any transition effects when changing routes.

There are several ways to add smooth transitions to your Vue.js Router animations:

1. Using the router-link component The simplest way to add a transition is by using the router-link component in combination with CSS transitions. You can use the transition attribute on the <router-link> tag to specify the name of the animation you want to apply.

Here's an example:

<template>
  <div id="app">
    <nav>
      <router-link to="/" exact transition="fade">Home</router-link>
      <router-link to="/about" transition="slide">About</router-link>
      <router-link to="/contact" transition="scale">Contact</router-link>
    </nav>

    <router-view></router-view>
  </div>
</template>

<script>
import FadeTransition from '@/transitions/FadeTransition.vue'
import SlideTransition from '@/transitions/SlideTransition.vue'
import ScaleTransition from '@/transitions/ScaleTransition.vue'

export default {
  components: {
    FadeTransition,
    SlideTransition,
    ScaleTransition
  }
}
</script>

In this example, we have three router-link components with different transition names (fade, slide, and scale). We also import the corresponding Vue components for each transition.

2. Using CSS Transitions You can use CSS transitions to create smooth animations when changing routes. You can apply a class to the <router-view> component, and then define a keyframes animation with that class.

Here's an example:

<template>
  <div id="app">
    <nav>
      <router-link to="/" exact>Home</router-link>
      <router-link to="/about">About</router-link>
      <router-link to="/contact">Contact</router-link>
    </nav>

    <router-view class="fade"></router-view>
  </div>
</template>

<style scoped>
.fade-enter-active,
.fade-leave-active {
  transition: opacity .5s;
}

.fade-enter,
.fade-leave-to {
  opacity: 0;
}
</style>

In this example, we have a <router-view> component with the class fade. We define two keyframes animations for the fade-enter and fade-leave-to states. The fade-enter-active and fade-leave-active classes are used to specify the transition duration.

3. Using Vue Router Transitions Vue.js Router also provides a built-in set of transitions that you can use out of the box. You can apply them by adding a <transition> component inside the <router-view>.

Here's an example:

<template>
  <div id="app">
    <nav>
      <router-link to="/" exact>Home</router-link>
      <router-link to="/about">About</router-link>
      <router-link to="/contact">Contact</router-link>
    </nav>

    <transition name="fade" mode="out-in">
      <router-view></router-view>
    </transition>
  </div>
</template>

<style scoped>
.fade-enter-active,
.fade-leave-active {
  transition: opacity .5s;
}

.fade-enter,
.fade-leave-to {
  opacity: 0;
}
</style>

In this example, we have a <transition> component inside the <router-view>. We specify the transition name as fade and set the mode attribute to out-in. This means that the transition will apply before leaving the previous route and after entering the new route.

I hope this helps you solve your Vue.js Router transition animation problems!