diff --git a/src/geometry/dual_quaternion_construction.rs b/src/geometry/dual_quaternion_construction.rs
index 2ec3d6b5..daedc239 100644
--- a/src/geometry/dual_quaternion_construction.rs
+++ b/src/geometry/dual_quaternion_construction.rs
@@ -1,3 +1,5 @@
+#[cfg(feature = "arbitrary")]
+use quickcheck::{Arbitrary, Gen};
 use crate::{
     DualQuaternion, Quaternion, UnitDualQuaternion, SimdRealField, Isometry3,
     Translation3, UnitQuaternion
@@ -97,6 +99,21 @@ where
     }
 }
 
+#[cfg(feature = "arbitrary")]
+impl<N> Arbitrary for DualQuaternion<N>
+where
+    N: SimdRealField + Arbitrary + Send,
+    N::Element: SimdRealField,
+{
+    #[inline]
+    fn arbitrary<G: Gen>(rng: &mut G) -> Self {
+        Self::from_real_and_dual(
+            Arbitrary::arbitrary(rng),
+            Arbitrary::arbitrary(rng)
+        )
+    }
+}
+
 impl<N: SimdRealField> UnitDualQuaternion<N> {
     /// The unit dual quaternion multiplicative identity, which also represents
     /// the identity transformation as an isometry.
@@ -195,3 +212,15 @@ where
         Self::identity()
     }
 }
+
+#[cfg(feature = "arbitrary")]
+impl<N> Arbitrary for UnitDualQuaternion<N>
+where
+    N: SimdRealField + Arbitrary + Send,
+    N::Element: SimdRealField,
+{
+    #[inline]
+    fn arbitrary<G: Gen>(rng: &mut G) -> Self {
+        Self::new_normalize(Arbitrary::arbitrary(rng))
+    }
+}
diff --git a/src/geometry/dual_quaternion_ops.rs b/src/geometry/dual_quaternion_ops.rs
index 95991c63..098fde6b 100644
--- a/src/geometry/dual_quaternion_ops.rs
+++ b/src/geometry/dual_quaternion_ops.rs
@@ -25,7 +25,7 @@
 use crate::{
     DualQuaternion, SimdRealField, Point3, Point, Vector3, Isometry3, Quaternion,
     UnitDualQuaternion, UnitQuaternion, U1, U3, U4, Unit, Allocator,
-    DefaultAllocator, Vector
+    DefaultAllocator, Vector, Translation3
 };
 use crate::base::storage::Storage;
 use std::mem;
@@ -362,6 +362,223 @@ dual_quaternion_op_impl!(
     Output = UnitDualQuaternion<N> => U3, U3;
     UnitDualQuaternion::<N>::new_unchecked(DualQuaternion::from_real(self.into_inner())) * rhs;);
 
+// UnitDualQuaternion ÷ UnitQuaternion
+dual_quaternion_op_impl!(
+    Div, div;
+    (U4, U1), (U4, U1);
+    self: &'a UnitDualQuaternion<N>, rhs: &'b UnitQuaternion<N>,
+    Output = UnitDualQuaternion<N> => U1, U4;
+    #[allow(clippy::suspicious_arithmetic_impl)]
+    { self * UnitDualQuaternion::<N>::from_rotation(rhs.inverse()) };
+    'a, 'b);
+
+dual_quaternion_op_impl!(
+    Div, div;
+    (U4, U1), (U4, U1);
+    self: &'a UnitDualQuaternion<N>, rhs: UnitQuaternion<N>,
+    Output = UnitDualQuaternion<N> => U3, U3;
+    #[allow(clippy::suspicious_arithmetic_impl)]
+    { self * UnitDualQuaternion::<N>::from_rotation(rhs.inverse()) };
+    'a);
+
+dual_quaternion_op_impl!(
+    Div, div;
+    (U4, U1), (U4, U1);
+    self: UnitDualQuaternion<N>, rhs: &'b UnitQuaternion<N>,
+    Output = UnitDualQuaternion<N> => U3, U3;
+    #[allow(clippy::suspicious_arithmetic_impl)]
+    { self * UnitDualQuaternion::<N>::from_rotation(rhs.inverse()) };
+    'b);
+
+dual_quaternion_op_impl!(
+    Div, div;
+    (U4, U1), (U4, U1);
+    self: UnitDualQuaternion<N>, rhs: UnitQuaternion<N>,
+    Output = UnitDualQuaternion<N> => U3, U3;
+    #[allow(clippy::suspicious_arithmetic_impl)]
+    { self * UnitDualQuaternion::<N>::from_rotation(rhs.inverse()) };);
+
+// UnitQuaternion ÷ UnitDualQuaternion
+dual_quaternion_op_impl!(
+    Div, div;
+    (U4, U1), (U4, U1);
+    self: &'a UnitQuaternion<N>, rhs: &'b UnitDualQuaternion<N>,
+    Output = UnitDualQuaternion<N> => U1, U4;
+    #[allow(clippy::suspicious_arithmetic_impl)]
+    {
+        UnitDualQuaternion::<N>::new_unchecked(
+            DualQuaternion::from_real(self.into_inner())
+        ) * rhs.inverse()
+    }; 'a, 'b);
+
+dual_quaternion_op_impl!(
+    Div, div;
+    (U4, U1), (U4, U1);
+    self: &'a UnitQuaternion<N>, rhs: UnitDualQuaternion<N>,
+    Output = UnitDualQuaternion<N> => U3, U3;
+    #[allow(clippy::suspicious_arithmetic_impl)]
+    {
+        UnitDualQuaternion::<N>::new_unchecked(
+            DualQuaternion::from_real(self.into_inner())
+        ) * rhs.inverse()
+    }; 'a);
+
+dual_quaternion_op_impl!(
+    Div, div;
+    (U4, U1), (U4, U1);
+    self: UnitQuaternion<N>, rhs: &'b UnitDualQuaternion<N>,
+    Output = UnitDualQuaternion<N> => U3, U3;
+    #[allow(clippy::suspicious_arithmetic_impl)]
+    {
+        UnitDualQuaternion::<N>::new_unchecked(
+            DualQuaternion::from_real(self.into_inner())
+        ) * rhs.inverse()
+    }; 'b);
+
+dual_quaternion_op_impl!(
+    Div, div;
+    (U4, U1), (U4, U1);
+    self: UnitQuaternion<N>, rhs: UnitDualQuaternion<N>,
+    Output = UnitDualQuaternion<N> => U3, U3;
+    #[allow(clippy::suspicious_arithmetic_impl)]
+    {
+        UnitDualQuaternion::<N>::new_unchecked(
+            DualQuaternion::from_real(self.into_inner())
+        ) * rhs.inverse()
+    };);
+
+// UnitDualQuaternion × Translation3
+dual_quaternion_op_impl!(
+    Mul, mul;
+    (U4, U1), (U3, U1);
+    self: &'a UnitDualQuaternion<N>, rhs: &'b Translation3<N>,
+    Output = UnitDualQuaternion<N> => U3, U1;
+    self * UnitDualQuaternion::<N>::from_parts(rhs.clone(), UnitQuaternion::identity());
+    'a, 'b);
+
+dual_quaternion_op_impl!(
+    Mul, mul;
+    (U4, U1), (U3, U3);
+    self: &'a UnitDualQuaternion<N>, rhs: Translation3<N>,
+    Output = UnitDualQuaternion<N> => U3, U1;
+    self * UnitDualQuaternion::<N>::from_parts(rhs, UnitQuaternion::identity());
+    'a);
+
+dual_quaternion_op_impl!(
+    Mul, mul;
+    (U4, U1), (U3, U3);
+    self: UnitDualQuaternion<N>, rhs: &'b Translation3<N>,
+    Output = UnitDualQuaternion<N> => U3, U1;
+    self * UnitDualQuaternion::<N>::from_parts(rhs.clone(), UnitQuaternion::identity());
+    'b);
+
+dual_quaternion_op_impl!(
+    Mul, mul;
+    (U4, U1), (U3, U3);
+    self: UnitDualQuaternion<N>, rhs: Translation3<N>,
+    Output = UnitDualQuaternion<N> => U3, U1;
+    self * UnitDualQuaternion::<N>::from_parts(rhs, UnitQuaternion::identity()); );
+
+// UnitDualQuaternion ÷ Translation3
+dual_quaternion_op_impl!(
+    Div, div;
+    (U4, U1), (U3, U1);
+    self: &'a UnitDualQuaternion<N>, rhs: &'b Translation3<N>,
+    Output = UnitDualQuaternion<N> => U3, U1;
+    #[allow(clippy::suspicious_arithmetic_impl)]
+    { self * UnitDualQuaternion::<N>::from_parts(rhs.inverse(), UnitQuaternion::identity()) };
+    'a, 'b);
+
+dual_quaternion_op_impl!(
+    Div, div;
+    (U4, U1), (U3, U3);
+    self: &'a UnitDualQuaternion<N>, rhs: Translation3<N>,
+    Output = UnitDualQuaternion<N> => U3, U1;
+    #[allow(clippy::suspicious_arithmetic_impl)]
+    { self * UnitDualQuaternion::<N>::from_parts(rhs.inverse(), UnitQuaternion::identity()) };
+    'a);
+
+dual_quaternion_op_impl!(
+    Div, div;
+    (U4, U1), (U3, U3);
+    self: UnitDualQuaternion<N>, rhs: &'b Translation3<N>,
+    Output = UnitDualQuaternion<N> => U3, U1;
+    #[allow(clippy::suspicious_arithmetic_impl)]
+    { self * UnitDualQuaternion::<N>::from_parts(rhs.inverse(), UnitQuaternion::identity()) };
+    'b);
+
+dual_quaternion_op_impl!(
+    Div, div;
+    (U4, U1), (U3, U3);
+    self: UnitDualQuaternion<N>, rhs: Translation3<N>,
+    Output = UnitDualQuaternion<N> => U3, U1;
+    #[allow(clippy::suspicious_arithmetic_impl)]
+    { self * UnitDualQuaternion::<N>::from_parts(rhs.inverse(), UnitQuaternion::identity()) };);
+
+// Translation3 × UnitDualQuaternion
+dual_quaternion_op_impl!(
+    Mul, mul;
+    (U3, U1), (U4, U1);
+    self: &'b Translation3<N>, rhs: &'a UnitDualQuaternion<N>,
+    Output = UnitDualQuaternion<N> => U3, U1;
+    UnitDualQuaternion::<N>::from_parts(self.clone(), UnitQuaternion::identity()) * rhs;
+    'a, 'b);
+
+dual_quaternion_op_impl!(
+    Mul, mul;
+    (U3, U1), (U4, U1);
+    self: &'a Translation3<N>, rhs: UnitDualQuaternion<N>,
+    Output = UnitDualQuaternion<N> => U3, U1;
+    UnitDualQuaternion::<N>::from_parts(self.clone(), UnitQuaternion::identity()) * rhs;
+    'a);
+
+dual_quaternion_op_impl!(
+    Mul, mul;
+    (U3, U1), (U4, U1);
+    self: Translation3<N>, rhs: &'b UnitDualQuaternion<N>,
+    Output = UnitDualQuaternion<N> => U3, U1;
+    UnitDualQuaternion::<N>::from_parts(self, UnitQuaternion::identity()) * rhs;
+    'b);
+
+dual_quaternion_op_impl!(
+    Mul, mul;
+    (U3, U1), (U4, U1);
+    self: Translation3<N>, rhs: UnitDualQuaternion<N>,
+    Output = UnitDualQuaternion<N> => U3, U1;
+    UnitDualQuaternion::<N>::from_parts(self, UnitQuaternion::identity()) * rhs;);
+
+// Translation3 ÷ UnitDualQuaternion
+dual_quaternion_op_impl!(
+    Div, div;
+    (U3, U1), (U4, U1);
+    self: &'b Translation3<N>, rhs: &'a UnitDualQuaternion<N>,
+    Output = UnitDualQuaternion<N> => U3, U1;
+    UnitDualQuaternion::<N>::from_parts(self.clone(), UnitQuaternion::identity()) / rhs;
+    'a, 'b);
+
+dual_quaternion_op_impl!(
+    Div, div;
+    (U3, U1), (U4, U1);
+    self: &'a Translation3<N>, rhs: UnitDualQuaternion<N>,
+    Output = UnitDualQuaternion<N> => U3, U1;
+    UnitDualQuaternion::<N>::from_parts(self.clone(), UnitQuaternion::identity()) / rhs;
+    'a);
+
+dual_quaternion_op_impl!(
+    Div, div;
+    (U3, U1), (U4, U1);
+    self: Translation3<N>, rhs: &'b UnitDualQuaternion<N>,
+    Output = UnitDualQuaternion<N> => U3, U1;
+    UnitDualQuaternion::<N>::from_parts(self, UnitQuaternion::identity()) / rhs;
+    'b);
+
+dual_quaternion_op_impl!(
+    Div, div;
+    (U3, U1), (U4, U1);
+    self: Translation3<N>, rhs: UnitDualQuaternion<N>,
+    Output = UnitDualQuaternion<N> => U3, U1;
+    UnitDualQuaternion::<N>::from_parts(self, UnitQuaternion::identity()) / rhs;);
+
 // UnitDualQuaternion × Isometry3
 dual_quaternion_op_impl!(
     Mul, mul;
@@ -738,6 +955,78 @@ dual_quaternion_op_impl!(
     self: UnitDualQuaternion<N>, rhs: UnitDualQuaternion<N>;
     *self /= &rhs; );
 
+// UnitDualQuaternion ×= UnitQuaternion
+dual_quaternion_op_impl!(
+    MulAssign, mul_assign;
+    (U4, U1), (U4, U1);
+    self: UnitDualQuaternion<N>, rhs: UnitQuaternion<N>;
+    {
+        let res = &*self * UnitDualQuaternion::from_rotation(rhs);
+        self.as_mut_unchecked().real.coords.copy_from(&res.as_ref().real.coords);
+        self.as_mut_unchecked().dual.coords.copy_from(&res.as_ref().dual.coords);
+    };);
+
+dual_quaternion_op_impl!(
+    MulAssign, mul_assign;
+    (U4, U1), (U4, U1);
+    self: UnitDualQuaternion<N>, rhs: &'b UnitQuaternion<N>;
+    *self *= rhs.clone(); 'b);
+
+// UnitDualQuaternion ÷= UnitQuaternion
+dual_quaternion_op_impl!(
+    DivAssign, div_assign;
+    (U4, U1), (U4, U1);
+    self: UnitDualQuaternion<N>, rhs: &'b UnitQuaternion<N>;
+    #[allow(clippy::suspicious_arithmetic_impl)]
+    {
+        let res = &*self * UnitDualQuaternion::from_rotation(rhs.inverse());
+        self.as_mut_unchecked().real.coords.copy_from(&res.as_ref().real.coords);
+        self.as_mut_unchecked().dual.coords.copy_from(&res.as_ref().dual.coords);
+    };
+    'b);
+
+dual_quaternion_op_impl!(
+    DivAssign, div_assign;
+    (U4, U1), (U4, U1);
+    self: UnitDualQuaternion<N>, rhs: UnitQuaternion<N>;
+    *self /= &rhs; );
+
+// UnitDualQuaternion ×= Translation3
+dual_quaternion_op_impl!(
+    MulAssign, mul_assign;
+    (U4, U1), (U4, U1);
+    self: UnitDualQuaternion<N>, rhs: Translation3<N>;
+    {
+        let res = &*self * UnitDualQuaternion::from_parts(rhs, UnitQuaternion::identity());
+        self.as_mut_unchecked().real.coords.copy_from(&res.as_ref().real.coords);
+        self.as_mut_unchecked().dual.coords.copy_from(&res.as_ref().dual.coords);
+    };);
+
+dual_quaternion_op_impl!(
+    MulAssign, mul_assign;
+    (U4, U1), (U4, U1);
+    self: UnitDualQuaternion<N>, rhs: &'b Translation3<N>;
+    *self *= rhs.clone(); 'b);
+
+// UnitDualQuaternion ÷= Translation3
+dual_quaternion_op_impl!(
+    DivAssign, div_assign;
+    (U4, U1), (U4, U1);
+    self: UnitDualQuaternion<N>, rhs: &'b Translation3<N>;
+    #[allow(clippy::suspicious_arithmetic_impl)]
+    {
+        let res = &*self * UnitDualQuaternion::from_parts(rhs.inverse(), UnitQuaternion::identity());
+        self.as_mut_unchecked().real.coords.copy_from(&res.as_ref().real.coords);
+        self.as_mut_unchecked().dual.coords.copy_from(&res.as_ref().dual.coords);
+    };
+    'b);
+
+dual_quaternion_op_impl!(
+    DivAssign, div_assign;
+    (U4, U1), (U4, U1);
+    self: UnitDualQuaternion<N>, rhs: Translation3<N>;
+    *self /= &rhs; );
+
 // UnitDualQuaternion ×= Isometry3
 dual_quaternion_op_impl!(
     MulAssign, mul_assign;
diff --git a/tests/geometry/dual_quaternion.rs b/tests/geometry/dual_quaternion.rs
new file mode 100644
index 00000000..1baced29
--- /dev/null
+++ b/tests/geometry/dual_quaternion.rs
@@ -0,0 +1,172 @@
+#![cfg(feature = "arbitrary")]
+#![allow(non_snake_case)]
+
+use na::{
+    Isometry3, Point3, Translation3, UnitQuaternion, UnitDualQuaternion, Vector3,
+};
+
+quickcheck!(
+    fn isometry_equivalence(iso: Isometry3<f64>, p: Point3<f64>, v: Vector3<f64>) -> bool {
+        let dq = UnitDualQuaternion::from_isometry(&iso);
+
+        relative_eq!(iso * p, dq * p, epsilon = 1.0e-7)
+            && relative_eq!(iso * v, dq * v, epsilon = 1.0e-7)
+    }
+
+    fn inverse_is_identity(i: UnitDualQuaternion<f64>, p: Point3<f64>, v: Vector3<f64>) -> bool {
+        let ii = i.inverse();
+
+        relative_eq!(i * ii, UnitDualQuaternion::identity(), epsilon = 1.0e-7)
+            && relative_eq!(ii * i, UnitDualQuaternion::identity(), epsilon = 1.0e-7)
+            && relative_eq!((i * ii) * p, p, epsilon = 1.0e-7)
+            && relative_eq!((ii * i) * p, p, epsilon = 1.0e-7)
+            && relative_eq!((i * ii) * v, v, epsilon = 1.0e-7)
+            && relative_eq!((ii * i) * v, v, epsilon = 1.0e-7)
+    }
+
+    fn multiply_equals_alga_transform(
+        dq: UnitDualQuaternion<f64>, v: Vector3<f64>, p: Point3<f64>
+    ) -> bool {
+        dq * v == dq.transform_vector(&v)
+            && dq * p == dq.transform_point(&p)
+            && relative_eq!(
+                dq.inverse() * v,
+                dq.inverse_transform_vector(&v),
+                epsilon = 1.0e-7
+            )
+            && relative_eq!(
+                dq.inverse() * p,
+                dq.inverse_transform_point(&p),
+                epsilon = 1.0e-7
+            )
+    }
+
+    #[cfg_attr(rustfmt, rustfmt_skip)]
+    fn composition(
+        dq: UnitDualQuaternion<f64>,
+        uq: UnitQuaternion<f64>,
+        t: Translation3<f64>,
+        v: Vector3<f64>,
+        p: Point3<f64>
+    ) -> bool {
+        // (rotation × dual quaternion) * point = rotation × (dual quaternion * point)
+        relative_eq!((uq * dq) * v, uq * (dq * v), epsilon = 1.0e-7) &&
+        relative_eq!((uq * dq) * p, uq * (dq * p), epsilon = 1.0e-7) &&
+
+        // (dual quaternion × rotation) * point = dual quaternion × (rotation * point)
+        relative_eq!((dq * uq) * v, dq * (uq * v), epsilon = 1.0e-7) &&
+        relative_eq!((dq * uq) * p, dq * (uq * p), epsilon = 1.0e-7) &&
+
+        // (translation × dual quaternion) * point = translation × (dual quaternion * point)
+        relative_eq!((t * dq) * v,     (dq * v), epsilon = 1.0e-7) &&
+        relative_eq!((t * dq) * p, t * (dq * p), epsilon = 1.0e-7) &&
+
+        // (dual quaternion × translation) * point = dual quaternion × (translation * point)
+        relative_eq!((dq * t) * v, dq * v,       epsilon = 1.0e-7) &&
+        relative_eq!((dq * t) * p, dq * (t * p), epsilon = 1.0e-7)
+    }
+
+    #[cfg_attr(rustfmt, rustfmt_skip)]
+    fn all_op_exist(
+        dq: UnitDualQuaternion<f64>,
+        uq: UnitQuaternion<f64>,
+        t: Translation3<f64>,
+        v: Vector3<f64>,
+        p: Point3<f64>
+    ) -> bool {
+        let iMi = dq * dq;
+        let iMuq = dq * uq;
+        let iDi = dq / dq;
+        let iDuq = dq / uq;
+
+        let iMp = dq * p;
+        let iMv = dq * v;
+
+        let iMt = dq * t;
+        let tMi = t * dq;
+
+        let tMuq = t * uq;
+
+        let uqMi = uq * dq;
+        let uqDi = uq / dq;
+
+        let uqMt = uq * t;
+
+        let mut iMt1 = dq;
+        let mut iMt2 = dq;
+
+        let mut iMi1 = dq;
+        let mut iMi2 = dq;
+
+        let mut iMuq1 = dq;
+        let mut iMuq2 = dq;
+
+        let mut iDi1 = dq;
+        let mut iDi2 = dq;
+
+        let mut iDuq1 = dq;
+        let mut iDuq2 = dq;
+
+        iMt1 *= t;
+        iMt2 *= &t;
+
+        iMi1 *= dq;
+        iMi2 *= &dq;
+
+        iMuq1 *= uq;
+        iMuq2 *= &uq;
+
+        iDi1 /= dq;
+        iDi2 /= &dq;
+
+        iDuq1 /= uq;
+        iDuq2 /= &uq;
+
+        iMt == iMt1
+            && iMt == iMt2
+            && iMi == iMi1
+            && iMi == iMi2
+            && iMuq == iMuq1
+            && iMuq == iMuq2
+            && iDi == iDi1
+            && iDi == iDi2
+            && iDuq == iDuq1
+            && iDuq == iDuq2
+            && iMi == &dq * &dq
+            && iMi == dq * &dq
+            && iMi == &dq * dq
+            && iMuq == &dq * &uq
+            && iMuq == dq * &uq
+            && iMuq == &dq * uq
+            && iDi == &dq / &dq
+            && iDi == dq / &dq
+            && iDi == &dq / dq
+            && iDuq == &dq / &uq
+            && iDuq == dq / &uq
+            && iDuq == &dq / uq
+            && iMp == &dq * &p
+            && iMp == dq * &p
+            && iMp == &dq * p
+            && iMv == &dq * &v
+            && iMv == dq * &v
+            && iMv == &dq * v
+            && iMt == &dq * &t
+            && iMt == dq * &t
+            && iMt == &dq * t
+            && tMi == &t * &dq
+            && tMi == t * &dq
+            && tMi == &t * dq
+            && tMuq == &t * &uq
+            && tMuq == t * &uq
+            && tMuq == &t * uq
+            && uqMi == &uq * &dq
+            && uqMi == uq * &dq
+            && uqMi == &uq * dq
+            && uqDi == &uq / &dq
+            && uqDi == uq / &dq
+            && uqDi == &uq / dq
+            && uqMt == &uq * &t
+            && uqMt == uq * &t
+            && uqMt == &uq * t
+    }
+);
diff --git a/tests/geometry/mod.rs b/tests/geometry/mod.rs
index ec9755a0..68d1bd6e 100644
--- a/tests/geometry/mod.rs
+++ b/tests/geometry/mod.rs
@@ -5,3 +5,4 @@ mod quaternion;
 mod rotation;
 mod similarity;
 mod unit_complex;
+mod dual_quaternion;