diff --git a/pyproject.toml b/pyproject.toml
index 23168906..1d07e912 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -58,7 +58,8 @@ dev = [
     "pytest-timeout",
     "pytest-xvfb",
     "coverage",
-    "flake8"
+    "flake8",
+    "mypy>=0.981",
 ]
 
 docs = [
diff --git a/spatialmath/DualQuaternion.py b/spatialmath/DualQuaternion.py
index 3b945d7c..1ea7862f 100644
--- a/spatialmath/DualQuaternion.py
+++ b/spatialmath/DualQuaternion.py
@@ -1,5 +1,7 @@
 from __future__ import annotations
 import numpy as np
+from typing import Optional
+
 from spatialmath import Quaternion, UnitQuaternion, SE3
 from spatialmath import base
 from spatialmath.base.types import *
@@ -30,7 +32,7 @@ class DualQuaternion:
     :seealso: :func:`UnitDualQuaternion`
     """
 
-    def __init__(self, real: Quaternion = None, dual: Quaternion = None):
+    def __init__(self, real: Quaternion, dual: Optional[Quaternion] = None):
         """
         Construct a new dual quaternion
 
@@ -55,14 +57,10 @@ def __init__(self, real: Quaternion = None, dual: Quaternion = None):
 
         """
 
-        if real is None and dual is None:
-            self.real = None
-            self.dual = None
-            return
-        elif dual is None and base.isvector(real, 8):
+        if dual is None and base.isvector(real, 8):
             self.real = Quaternion(real[0:4])
             self.dual = Quaternion(real[4:8])
-        elif real is not None and dual is not None:
+        elif dual is not None:
             if not isinstance(real, Quaternion):
                 raise ValueError("real part must be a Quaternion subclass")
             if not isinstance(dual, Quaternion):
@@ -70,7 +68,7 @@ def __init__(self, real: Quaternion = None, dual: Quaternion = None):
             self.real = real  # quaternion, real part
             self.dual = dual  # quaternion, dual part
         else:
-            raise ValueError("expecting zero or two parameters")
+            raise ValueError("expecting one or two parameters")
 
     @classmethod
     def Pure(cls, x: ArrayLike3) -> Self:
@@ -119,7 +117,7 @@ def norm(self) -> Tuple[float, float]:
         b = self.real * self.dual.conj() + self.dual * self.real.conj()
         return (base.sqrt(a.s), base.sqrt(b.s))
 
-    def conj(self) -> Self:
+    def conj(self) -> DualQuaternion:
         r"""
         Conjugate of dual quaternion
 
@@ -142,7 +140,7 @@ def conj(self) -> Self:
 
     def __add__(
         left, right: DualQuaternion
-    ) -> Self:  # pylint: disable=no-self-argument
+    ) -> DualQuaternion:  # pylint: disable=no-self-argument
         """
         Sum of two dual quaternions
 
@@ -161,7 +159,7 @@ def __add__(
 
     def __sub__(
         left, right: DualQuaternion
-    ) -> Self:  # pylint: disable=no-self-argument
+    ) -> DualQuaternion:  # pylint: disable=no-self-argument
         """
         Difference of two dual quaternions
 
@@ -178,7 +176,7 @@ def __sub__(
         """
         return DualQuaternion(left.real - right.real, left.dual - right.dual)
 
-    def __mul__(left, right: Self) -> Self:  # pylint: disable=no-self-argument
+    def __mul__(left, right: Self) -> DualQuaternion:  # pylint: disable=no-self-argument
         """
         Product of dual quaternion
 
@@ -271,13 +269,14 @@ class UnitDualQuaternion(DualQuaternion):
     """
 
     @overload
-    def __init__(self, T: SE3):
+    def __init__(self, real: SE3, dual: None = None):
         ...
 
+    @overload
     def __init__(self, real: Quaternion, dual: Quaternion):
         ...
 
-    def __init__(self, real=None, dual=None):
+    def __init__(self, real, dual=None):
         r"""
         Create new unit dual quaternion
 
diff --git a/spatialmath/base/__init__.py b/spatialmath/base/__init__.py
index 98ff87f0..85e0dbed 100644
--- a/spatialmath/base/__init__.py
+++ b/spatialmath/base/__init__.py
@@ -286,6 +286,8 @@
     "iseye",
     "skew",
     "vex",
+    "skewa2",
+    "skewa3",
     "skewa",
     "vexa",
     "h2e",
diff --git a/spatialmath/base/_types_311.py b/spatialmath/base/_types_311.py
index bd1d64b9..384d9e55 100644
--- a/spatialmath/base/_types_311.py
+++ b/spatialmath/base/_types_311.py
@@ -1,4 +1,8 @@
-# for Python >= 3.9
+# for Python >= 3.11
+
+import sys
+
+assert sys.version_info >= (3, 11)
 
 from typing import (
     overload,
diff --git a/spatialmath/base/_types_39.py b/spatialmath/base/_types_39.py
index 350210f5..ab5a0a63 100644
--- a/spatialmath/base/_types_39.py
+++ b/spatialmath/base/_types_39.py
@@ -1,5 +1,9 @@
 # for Python >= 3.9
 
+import sys
+
+assert sys.version_info >= (3, 9)
+
 from typing import (
     overload,
     cast,
@@ -116,36 +120,21 @@
 RNx3 = NDArray
 
 # Lie group elements
-SO2Array = ndarray[Tuple[L[2, 2]], dtype[floating]]  # SO(2) rotation matrix
-SE2Array = ndarray[Tuple[L[3, 3]], dtype[floating]]  # SE(2) rigid-body transform
-# SO3Array = ndarray[Tuple[L[3, 3]], dtype[floating]]
-SO3Array = np.ndarray[Tuple[L[3], L[3]], dtype[floating]]  # SO(3) rotation matrix
-SE3Array = ndarray[Tuple[L[4], L[4]], dtype[floating]]  # SE(3) rigid-body transform
+SO2Array = R2x2  # SO(2) rotation matrix
+SE2Array = R3x3  # SE(2) rigid-body transform
+SO3Array = R3x3  # SO(3) rotation matrix
+SE3Array = R4x4  # SE(3) rigid-body transform
 
 
 # Lie algebra elements
-so2Array = ndarray[
-    Tuple[L[2, 2]], dtype[floating]
-]  # so(2) Lie algebra of SO(2), skew-symmetrix matrix
-se2Array = ndarray[
-    Tuple[L[3, 3]], dtype[floating]
-]  # se(2) Lie algebra of SE(2), augmented skew-symmetrix matrix
-so3Array = ndarray[
-    Tuple[L[3, 3]], dtype[floating]
-]  # so(3) Lie algebra of SO(3), skew-symmetrix matrix
-se3Array = ndarray[
-    Tuple[L[4, 4]], dtype[floating]
-]  # se(3) Lie algebra of SE(3), augmented skew-symmetrix matrix
+so2Array = R2x2  # so(2) Lie algebra of SO(2), skew-symmetrix matrix
+se2Array = R3x3  # se(2) Lie algebra of SE(2), augmented skew-symmetrix matrix
+so3Array = R3x3  # so(3) Lie algebra of SO(3), skew-symmetrix matrix
+se3Array = R4x4  # se(3) Lie algebra of SE(3), augmented skew-symmetrix matrix
 
 # quaternion arrays
-QuaternionArray = ndarray[
-    Tuple[L[4,]],
-    dtype[floating],
-]
-UnitQuaternionArray = ndarray[
-    Tuple[L[4,]],
-    dtype[floating],
-]
+QuaternionArray = R4
+UnitQuaternionArray = R4
 
 Rn = Union[R2, R3]
 
diff --git a/spatialmath/base/animate.py b/spatialmath/base/animate.py
index a2e31f72..1f8b6c47 100755
--- a/spatialmath/base/animate.py
+++ b/spatialmath/base/animate.py
@@ -11,7 +11,7 @@
 from __future__ import annotations
 import os.path
 import numpy as np
-import matplotlib.pyplot as plt
+import matplotlib.pyplot as plt # type: ignore
 from matplotlib import animation
 import spatialmath.base as smb
 from collections.abc import Iterable, Iterator
diff --git a/spatialmath/base/argcheck.py b/spatialmath/base/argcheck.py
index 40f94336..b0b4464b 100644
--- a/spatialmath/base/argcheck.py
+++ b/spatialmath/base/argcheck.py
@@ -14,6 +14,7 @@
 import math
 import numpy as np
 from collections.abc import Iterable
+from typing import Literal
 
 # from spatialmath.base import symbolic as sym # HACK
 from spatialmath.base.symbolic import issymbol, symtype
@@ -281,7 +282,7 @@ def verifymatrix(
 def getvector(
     v: ArrayLike,
     dim: Optional[Union[int, None]] = None,
-    out: str = "array",
+    out: Literal["array"] = "array",
     dtype: DTypeLike = np.float64,
 ) -> NDArray:
     ...
@@ -291,7 +292,7 @@ def getvector(
 def getvector(
     v: ArrayLike,
     dim: Optional[Union[int, None]] = None,
-    out: str = "list",
+    out: Literal["list"] = "list",
     dtype: DTypeLike = np.float64,
 ) -> List[float]:
     ...
@@ -301,7 +302,7 @@ def getvector(
 def getvector(
     v: Tuple[float, ...],
     dim: Optional[Union[int, None]] = None,
-    out: str = "sequence",
+    out: Literal["sequence"] = "sequence",
     dtype: DTypeLike = np.float64,
 ) -> Tuple[float, ...]:
     ...
diff --git a/spatialmath/base/graphics.py b/spatialmath/base/graphics.py
index 2ce18dc8..87c83595 100644
--- a/spatialmath/base/graphics.py
+++ b/spatialmath/base/graphics.py
@@ -2,7 +2,7 @@
 from itertools import product
 import warnings
 import numpy as np
-from matplotlib import colors
+from matplotlib import colors # type: ignore
 
 from spatialmath import base as smb
 from spatialmath.base.types import *
@@ -23,14 +23,14 @@
 """
 
 try:
-    import matplotlib.pyplot as plt
-    from matplotlib.patches import Circle
-    from mpl_toolkits.mplot3d.art3d import (
+    import matplotlib.pyplot as plt # type: ignore
+    from matplotlib.patches import Circle # type: ignore
+    from mpl_toolkits.mplot3d.art3d import ( # type: ignore
         Poly3DCollection,
         Line3DCollection,
         pathpatch_2d_to_3d,
     )
-    from mpl_toolkits.mplot3d import Axes3D
+    from mpl_toolkits.mplot3d import Axes3D # type: ignore
 
     # TODO
     # return a redrawer object, that can be used for animation
@@ -327,7 +327,7 @@ def plot_homline(
         return handles
 
     def plot_box(
-        *fmt: Optional[str],
+        *fmt: List[str],
         lbrt: Optional[ArrayLike4] = None,
         lrbt: Optional[ArrayLike4] = None,
         lbwh: Optional[ArrayLike4] = None,
@@ -796,13 +796,13 @@ def ellipse(
             so to avoid inverting ``E`` twice to compute the ellipse, we flag that
             the inverse is provided using ``inverted``.
         """
-        from scipy.linalg import sqrtm
+        from scipy.linalg import sqrtm # type: ignore
 
         if E.shape != (2, 2):
             raise ValueError("ellipse is defined by a 2x2 matrix")
 
         if confidence:
-            from scipy.stats.distributions import chi2
+            from scipy.stats.distributions import chi2 # type: ignore
 
             # process the probability
             s = math.sqrt(chi2.ppf(confidence, df=2)) * scale
@@ -1570,7 +1570,7 @@ def axes_logic(
         return ax
 
     def plotvol2(
-        dim: ArrayLike = None,
+        dim: Optional[ArrayLike] = None,
         ax: Optional[plt.Axes] = None,
         equal: Optional[bool] = True,
         grid: Optional[bool] = False,
@@ -1625,7 +1625,7 @@ def plotvol2(
         return ax
 
     def plotvol3(
-        dim: ArrayLike = None,
+        dim: Optional[ArrayLike] = None,
         ax: Optional[plt.Axes] = None,
         equal: Optional[bool] = True,
         grid: Optional[bool] = False,
@@ -1685,7 +1685,7 @@ def plotvol3(
         ax._plotvol = True
         return ax
 
-    def expand_dims(dim: ArrayLike = None, nd: int = 2) -> NDArray:
+    def expand_dims(dim: Optional[ArrayLike] = None, nd: int = 2) -> NDArray:
         """
         Expand compact axis dimensions
 
diff --git a/spatialmath/base/quaternions.py b/spatialmath/base/quaternions.py
index 8f33bc1c..940a64c8 100755
--- a/spatialmath/base/quaternions.py
+++ b/spatialmath/base/quaternions.py
@@ -16,7 +16,7 @@
 import spatialmath.base as smb
 from spatialmath.base.argcheck import getunit
 from spatialmath.base.types import *
-import scipy.interpolate as interpolate
+import scipy.interpolate as interpolate # type: ignore
 from typing import Optional
 from functools import lru_cache
 
@@ -173,27 +173,12 @@ def qisunit(q: ArrayLike4, tol: float = 20) -> bool:
     return smb.iszerovec(q, tol=tol)
 
 
-@overload
 def qisequal(
-    q1: ArrayLike4,
-    q2: ArrayLike4,
-    tol: float = 20,
-    unitq: Optional[bool] = False,
-) -> bool:
-    ...
-
-
-@overload
-def qisequal(
-    q1: ArrayLike4,
-    q2: ArrayLike4,
-    tol: float = 20,
-    unitq: Optional[bool] = True,
-) -> bool:
-    ...
-
-
-def qisequal(q1, q2, tol: float = 20, unitq: Optional[bool] = False):
+        q1: ArrayLike4,
+        q2: ArrayLike4,
+        tol: float = 20,
+        unitq: Optional[bool] = False,
+):
     """
     Test if quaternions are equal
 
diff --git a/spatialmath/base/symbolic.py b/spatialmath/base/symbolic.py
index 2d92f4d4..3f03e6f5 100644
--- a/spatialmath/base/symbolic.py
+++ b/spatialmath/base/symbolic.py
@@ -16,10 +16,10 @@
 
 try:  # pragma: no cover
     # print('Using SymPy')
-    import sympy
+    import sympy # type: ignore
 
     _symbolics = True
-    symtype = (sympy.Expr,)
+    symtype : Tuple[type, ...] = (sympy.Expr,)
     from sympy import Symbol
 
 except ImportError:  # pragma: no cover
diff --git a/spatialmath/base/transforms2d.py b/spatialmath/base/transforms2d.py
index 682ea0ca..7d83371d 100644
--- a/spatialmath/base/transforms2d.py
+++ b/spatialmath/base/transforms2d.py
@@ -17,9 +17,10 @@
 import sys
 import math
 import numpy as np
+from typing import Literal
 
 try:
-    import matplotlib.pyplot as plt
+    import matplotlib.pyplot as plt # type: ignore
 
     _matplotlib_exists = True
 except ImportError:
@@ -34,7 +35,7 @@
 
 try:  # pragma: no cover
     # print('Using SymPy')
-    import sympy
+    import sympy # type: ignore
 
     _symbolics = True
 
@@ -443,7 +444,7 @@ def trinv2(T: SE2Array) -> SE2Array:
 @overload  # pragma: no cover
 def trlog2(
     T: SO2Array,
-    twist: bool = False,
+    twist: Literal[False] = False,
     check: bool = True,
     tol: float = 20,
 ) -> so2Array:
@@ -453,7 +454,7 @@ def trlog2(
 @overload  # pragma: no cover
 def trlog2(
     T: SE2Array,
-    twist: bool = False,
+    twist: Literal[False] = False,
     check: bool = True,
     tol: float = 20,
 ) -> se2Array:
@@ -463,7 +464,7 @@ def trlog2(
 @overload  # pragma: no cover
 def trlog2(
     T: SO2Array,
-    twist: bool = True,
+    twist: Literal[True] = True,
     check: bool = True,
     tol: float = 20,
 ) -> float:
@@ -473,7 +474,7 @@ def trlog2(
 @overload  # pragma: no cover
 def trlog2(
     T: SE2Array,
-    twist: bool = True,
+    twist: Literal[True] = True,
     check: bool = True,
     tol: float = 20,
 ) -> R3:
@@ -1131,7 +1132,7 @@ def ICP2d(
     # hack below to use points2tr above
     # use ClayFlannigan's improved data association
 
-    from scipy.spatial import KDTree
+    from scipy.spatial import KDTree # type: ignore
 
     def _FindCorrespondences(
         tree, source, reference
@@ -1226,7 +1227,7 @@ def _FindCorrespondences(
     import matplotlib.pyplot as plt
 
     # from mpl_toolkits.axisartist import Axes
-    from matplotlib.axes import Axes
+    from matplotlib.axes import Axes # type: ignore
 
     def trplot2(
         T: Union[SO2Array, SE2Array],
diff --git a/spatialmath/base/transforms3d.py b/spatialmath/base/transforms3d.py
index 3617f965..a5ed52bd 100644
--- a/spatialmath/base/transforms3d.py
+++ b/spatialmath/base/transforms3d.py
@@ -18,6 +18,7 @@
 from collections.abc import Iterable
 import math
 import numpy as np
+from typing import Literal
 
 from spatialmath.base.argcheck import getunit, getvector, isvector, isscalar, ismatrix
 from spatialmath.base.vectors import (
@@ -34,7 +35,7 @@
     t2r,
     rt2tr,
     skew,
-    skewa,
+    skewa3,
     vex,
     vexa,
     isskew,
@@ -1271,25 +1272,25 @@ def tr2rpy(
 # ---------------------------------------------------------------------------------------#
 @overload  # pragma: no cover
 def trlog(
-    T: SO3Array, check: bool = True, twist: bool = False, tol: float = 20
+    T: SO3Array, check: bool = True, twist: Literal[False] = False, tol: float = 20
 ) -> so3Array:
     ...
 
 
 @overload  # pragma: no cover
 def trlog(
-    T: SE3Array, check: bool = True, twist: bool = False, tol: float = 20
+    T: SE3Array, check: bool = True, twist: Literal[False] = False, tol: float = 20
 ) -> se3Array:
     ...
 
 
 @overload  # pragma: no cover
-def trlog(T: SO3Array, check: bool = True, twist: bool = True, tol: float = 20) -> R3:
+def trlog(T: SO3Array, check: bool = True, twist: Literal[True] = True, tol: float = 20) -> R3:
     ...
 
 
 @overload  # pragma: no cover
-def trlog(T: SE3Array, check: bool = True, twist: bool = True, tol: float = 20) -> R6:
+def trlog(T: SE3Array, check: bool = True, twist: Literal[True] = True, tol: float = 20) -> R6:
     ...
 
 
@@ -1405,26 +1406,92 @@ def trlog(
 
 # ---------------------------------------------------------------------------------------#
 @overload  # pragma: no cover
-def trexp(S: so3Array, theta: Optional[float] = None, check: bool = True) -> SO3Array:
+def trexp_SO3(S: so3Array, theta: Optional[float] = None, check: bool = True) -> SO3Array:
     ...
 
 
 @overload  # pragma: no cover
-def trexp(S: se3Array, theta: Optional[float] = None, check: bool = True) -> SE3Array:
+def trexp_SO3(S: ArrayLike3, theta: Optional[float] = None, check=True) -> SO3Array:
     ...
 
 
+def trexp_SO3(S, theta=None, check=True):
+    if ismatrix(S, (3, 3)) or isvector(S, 3):
+        # so(3) case
+        if ismatrix(S, (3, 3)):
+            # skew symmetric matrix
+            if check and not isskew(S):
+                raise ValueError("argument must be a valid so(3) element")
+            w = vex(S)
+        else:
+            # 3 vector
+            w = getvector(S)
+
+        if theta is not None and not isunitvec(w):
+            raise ValueError("If theta is specified S must be a unit twist")
+
+        # do Rodrigues' formula for rotation
+        return rodrigues(w, theta)
+    else:
+        raise ValueError(" First argument must be SO(3) or 3-vector")
+
+
 @overload  # pragma: no cover
-def trexp(S: ArrayLike3, theta: Optional[float] = None, check=True) -> SO3Array:
+def trexp_SE3(S: se3Array, theta: Optional[float] = None, check: bool = True) -> SE3Array:
     ...
 
 
 @overload  # pragma: no cover
-def trexp(S: ArrayLike6, theta: Optional[float] = None, check=True) -> SE3Array:
+def trexp_SE3(S: ArrayLike6, theta: Optional[float] = None, check=True) -> SE3Array:
     ...
 
 
-def trexp(S, theta=None, check=True):
+def trexp_SE3(S, theta=None, check=True):
+    if ismatrix(S, (4, 4)) or isvector(S, 6):
+        # se(3) case
+        if ismatrix(S, (4, 4)):
+            # augmentented skew matrix
+            if check and not isskewa(S):
+                raise ValueError("argument must be a valid se(3) element")
+            tw = vexa(cast(se3Array, S))
+        else:
+            # 6 vector
+            tw = getvector(S)
+
+        if iszerovec(tw):
+            return np.eye(4)
+
+        if theta is None:
+            (tw, theta) = unittwist_norm(tw)
+        else:
+            if theta == 0:
+                return np.eye(4)
+            elif not isunittwist(tw):
+                raise ValueError("If theta is specified S must be a unit twist")
+
+        # tw is a unit twist, th is its magnitude
+        t = tw[0:3]
+        w = tw[3:6]
+
+        R = rodrigues(w, theta)
+
+        skw = skew(w)
+        V = (
+            np.eye(3) * theta
+            + (1.0 - math.cos(theta)) * skw
+            + (theta - math.sin(theta)) * skw @ skw
+        )
+
+        return rt2tr(R, V @ t)
+    else:
+        raise ValueError(" First argument must be SE(3) or 6-vector")
+
+
+def trexp(
+        S: so3Array | ArrayLike3 | se3Array | ArrayLike6,
+        theta: Optional[float] = None,
+        check: bool = True,
+):
     """
     Exponential of se(3) or so(3) matrix
 
@@ -1485,58 +1552,9 @@ def trexp(S, theta=None, check=True):
     """
 
     if ismatrix(S, (4, 4)) or isvector(S, 6):
-        # se(3) case
-        if ismatrix(S, (4, 4)):
-            # augmentented skew matrix
-            if check and not isskewa(S):
-                raise ValueError("argument must be a valid se(3) element")
-            tw = vexa(cast(se3Array, S))
-        else:
-            # 6 vector
-            tw = getvector(S)
-
-        if iszerovec(tw):
-            return np.eye(4)
-
-        if theta is None:
-            (tw, theta) = unittwist_norm(tw)
-        else:
-            if theta == 0:
-                return np.eye(4)
-            elif not isunittwist(tw):
-                raise ValueError("If theta is specified S must be a unit twist")
-
-        # tw is a unit twist, th is its magnitude
-        t = tw[0:3]
-        w = tw[3:6]
-
-        R = rodrigues(w, theta)
-
-        skw = skew(w)
-        V = (
-            np.eye(3) * theta
-            + (1.0 - math.cos(theta)) * skw
-            + (theta - math.sin(theta)) * skw @ skw
-        )
-
-        return rt2tr(R, V @ t)
-
+        return trexp_SE3(S, theta=theta, check=check)
     elif ismatrix(S, (3, 3)) or isvector(S, 3):
-        # so(3) case
-        if ismatrix(S, (3, 3)):
-            # skew symmetric matrix
-            if check and not isskew(S):
-                raise ValueError("argument must be a valid so(3) element")
-            w = vex(S)
-        else:
-            # 3 vector
-            w = getvector(S)
-
-        if theta is not None and not isunitvec(w):
-            raise ValueError("If theta is specified S must be a unit twist")
-
-        # do Rodrigues' formula for rotation
-        return rodrigues(w, theta)
+        return trexp_SO3(S, theta=theta, check=check)
     else:
         raise ValueError(" First argument must be SO(3), 3-vector, SE(3) or 6-vector")
 
@@ -1722,7 +1740,7 @@ def delta2tr(d: R6) -> SE3Array:
     :SymPy: supported
     """
 
-    return np.eye(4, 4) + skewa(d)
+    return np.eye(4, 4) + skewa3(d)
 
 
 def trinv(T: SE3Array) -> SE3Array:
@@ -2121,7 +2139,7 @@ def x2r(r: ArrayLike3, representation: str = "rpy/xyz") -> SO3Array:
     elif representation in ("arm", "vehicle", "camera"):
         R = rpy2r(r, order=representation)
     elif representation == "exp":
-        R = trexp(r)
+        R = trexp_SO3(r)
     else:
         raise ValueError(f"unknown representation: {representation}")
     return R
@@ -2222,7 +2240,7 @@ def angvelxform_dot(𝚪, 𝚪d, full=True, representation="rpy/xyz"):
 def rotvelxform(
     𝚪: ArrayLike3,
     inverse: bool = False,
-    full: bool = False,
+    full: Literal[False] = False,
     representation="rpy/xyz",
 ) -> R3x3:
     ...
@@ -2232,7 +2250,7 @@ def rotvelxform(
 def rotvelxform(
     𝚪: SO3Array,
     inverse: bool = False,
-    full: bool = False,
+    full: Literal[False] = False,
 ) -> R3x3:
     ...
 
@@ -2241,7 +2259,7 @@ def rotvelxform(
 def rotvelxform(
     𝚪: ArrayLike3,
     inverse: bool = False,
-    full: bool = True,
+    full: Literal[True] = True,
     representation="rpy/xyz",
 ) -> R6x6:
     ...
@@ -2251,7 +2269,7 @@ def rotvelxform(
 def rotvelxform(
     𝚪: SO3Array,
     inverse: bool = False,
-    full: bool = True,
+    full: Literal[True] = True,
 ) -> R6x6:
     ...
 
@@ -2464,14 +2482,14 @@ def rotvelxform(
 
 @overload  # pragma: no cover
 def rotvelxform_inv_dot(
-    𝚪: ArrayLike3, 𝚪d: ArrayLike3, full: bool = False, representation: str = "rpy/xyz"
+    𝚪: ArrayLike3, 𝚪d: ArrayLike3, full: Literal[False] = False, representation: str = "rpy/xyz"
 ) -> R3x3:
     ...
 
 
 @overload  # pragma: no cover
 def rotvelxform_inv_dot(
-    𝚪: ArrayLike3, 𝚪d: ArrayLike3, full: bool = True, representation: str = "rpy/xyz"
+    𝚪: ArrayLike3, 𝚪d: ArrayLike3, full: Literal[True] = True, representation: str = "rpy/xyz"
 ) -> R6x6:
     ...
 
@@ -2908,8 +2926,8 @@ def _vec2s(fmt, v):
 
 
 try:
-    import matplotlib.pyplot as plt
-    from mpl_toolkits.mplot3d import Axes3D
+    import matplotlib.pyplot as plt # type: ignore
+    from mpl_toolkits.mplot3d import Axes3D # type: ignore
 
     _matplotlib_exists = True
 except ImportError:
diff --git a/spatialmath/base/transformsNd.py b/spatialmath/base/transformsNd.py
index c04e5d8b..54f0377b 100644
--- a/spatialmath/base/transformsNd.py
+++ b/spatialmath/base/transformsNd.py
@@ -24,7 +24,7 @@
 
 try:  # pragma: no cover
     # print('Using SymPy')
-    from sympy import Matrix
+    from sympy import Matrix # type: ignore
 
     _symbolics = True
 
@@ -590,14 +590,26 @@ def vex(s, check=False):
 
 
 # ---------------------------------------------------------------------------------------#
-@overload
-def skewa(v: ArrayLike3) -> se2Array:
-    ...
+def skewa2(v: ArrayLike3) -> se2Array:
+    v = getvector(v, None)
+    if len(v) == 3:
+        omega = np.zeros((3, 3), dtype=v.dtype)
+        omega[:2, :2] = skew(v[2])
+        omega[:2, 2] = v[0:2]
+        return omega
+    else:
+        raise ValueError("expecting a 3-vector")
 
 
-@overload
-def skewa(v: ArrayLike6) -> se3Array:
-    ...
+def skewa3(v: ArrayLike6) -> se3Array:
+    v = getvector(v, None)
+    if len(v) == 6:
+        omega = np.zeros((4, 4), dtype=v.dtype)
+        omega[:3, :3] = skew(v[3:6])
+        omega[:3, 3] = v[0:3]
+        return omega
+    else:
+        raise ValueError("expecting a 6-vector")
 
 
 def skewa(v: Union[ArrayLike3, ArrayLike6]) -> Union[se2Array, se3Array]:
@@ -633,15 +645,9 @@ def skewa(v: Union[ArrayLike3, ArrayLike6]) -> Union[se2Array, se3Array]:
 
     v = getvector(v, None)
     if len(v) == 3:
-        omega = np.zeros((3, 3), dtype=v.dtype)
-        omega[:2, :2] = skew(v[2])
-        omega[:2, 2] = v[0:2]
-        return omega
+        return skewa2(v)
     elif len(v) == 6:
-        omega = np.zeros((4, 4), dtype=v.dtype)
-        omega[:3, :3] = skew(v[3:6])
-        omega[:3, 3] = v[0:3]
-        return omega
+        return skewa3(v)
     else:
         raise ValueError("expecting a 3- or 6-vector")
 
diff --git a/spatialmath/base/types.py b/spatialmath/base/types.py
index eb35e9d2..2167855a 100644
--- a/spatialmath/base/types.py
+++ b/spatialmath/base/types.py
@@ -1,11 +1,8 @@
 import sys
 
-_version = sys.version_info.minor
-
-
-if _version >= 11:
+if sys.version_info >= (3, 11):
     from spatialmath.base._types_311 import *
-elif _version >= 9:
+elif sys.version_info >= (3, 9):
     from spatialmath.base._types_39 import *
 else:
     from spatialmath.base._types_35 import *
diff --git a/spatialmath/base/vectors.py b/spatialmath/base/vectors.py
index f29740a3..dffca21b 100644
--- a/spatialmath/base/vectors.py
+++ b/spatialmath/base/vectors.py
@@ -18,7 +18,7 @@
 
 try:  # pragma: no cover
     # print('Using SymPy')
-    import sympy
+    import sympy # type: ignore
 
     _symbolics = True
 
diff --git a/spatialmath/baseposelist.py b/spatialmath/baseposelist.py
index d729b902..509443c3 100644
--- a/spatialmath/baseposelist.py
+++ b/spatialmath/baseposelist.py
@@ -5,7 +5,7 @@
 # pylint: disable=invalid-name
 from __future__ import annotations
 from collections import UserList
-from abc import ABC, abstractproperty, abstractstaticmethod
+from abc import ABC, abstractproperty, abstractmethod
 import copy
 import numpy as np
 from spatialmath.base.argcheck import isnumberlist, isscalar
@@ -70,11 +70,12 @@ def shape(self):
         pass
 
     @staticmethod
-    @abstractstaticmethod
-    def isvalid(x, check=True):
+    @abstractmethod
+    def isvalid(x, check: bool=True) -> bool:
         pass
 
-    @abstractstaticmethod
+    @staticmethod
+    @abstractmethod
     def _identity():
         pass
 
@@ -362,17 +363,17 @@ def __setitem__(self, i: int, value: BasePoseList) -> None:
         self.data[i] = value.A
 
     # flag these binary operators as being not supported
-    def __lt__(self, other: BasePoseList) -> Type[Exception]:
-        return NotImplementedError
+    def __lt__(self, other):
+        raise NotImplementedError()
 
-    def __le__(self, other: BasePoseList) -> Type[Exception]:
-        return NotImplementedError
+    def __le__(self, other):
+        raise NotImplementedError()
 
-    def __gt__(self, other: BasePoseList) -> Type[Exception]:
-        return NotImplementedError
+    def __gt__(self, other):
+        raise NotImplementedError()
 
-    def __ge__(self, other: BasePoseList) -> Type[Exception]:
-        return NotImplementedError
+    def __ge__(self, other):
+        raise NotImplementedError()
 
     def append(self, item: BasePoseList) -> None:
         """
@@ -674,4 +675,4 @@ def unop(
     print(R.eulervec())
 
     R = SO2([0.3, 0.4, 0.5])
-    pass
\ No newline at end of file
+    pass
diff --git a/spatialmath/baseposematrix.py b/spatialmath/baseposematrix.py
index 1a850600..60ed6d09 100644
--- a/spatialmath/baseposematrix.py
+++ b/spatialmath/baseposematrix.py
@@ -23,7 +23,7 @@
 # colored printing of matrices to the terminal
 #   colored package has much finer control than colorama, but the latter is available by default with anaconda
 try:
-    from colored import fg, bg, attr
+    from colored import fg, bg, attr # type: ignore
 
     _colored = True
     # print('using colored output')
@@ -35,7 +35,7 @@
     _colored = False
 
 try:
-    from ansitable import ANSIMatrix
+    from ansitable import ANSIMatrix # type: ignore
 
     _ANSIMatrix = True
     # print('using colored output')
@@ -377,7 +377,7 @@ def log(self, twist: Optional[bool] = False) -> Union[NDArray, List[NDArray]]:
         else:
             return log
 
-    def interp(self, end: Optional[bool] = None, s: Union[int, float] = None, shortest: bool = True) -> Self:
+    def interp(self, end: Optional[bool] = None, s: Union[int, float, None] = None, shortest: bool = True) -> Self:
         """
         Interpolate between poses (superclass method)
 
@@ -443,7 +443,7 @@ def interp(self, end: Optional[bool] = None, s: Union[int, float] = None, shorte
                 [smb.trinterp(start=self.A, end=end, s=_s, shortest=shortest) for _s in s]
             )
 
-    def interp1(self, s: float = None) -> Self:
+    def interp1(self, s: Optional[float] = None) -> Self:
         """
         Interpolate pose (superclass method)
 
@@ -1572,7 +1572,7 @@ def __isub__(left, right: Self):  # pylint: disable=no-self-argument
         """
         return left.__sub__(right)
 
-    def __eq__(left, right: Self) -> bool:  # pylint: disable=no-self-argument
+    def __eq__(left, right):  # pylint: disable=no-self-argument
         """
         Overloaded ``==`` operator (superclass method)
 
diff --git a/spatialmath/geom2d.py b/spatialmath/geom2d.py
index 55eccb2a..b38a0115 100755
--- a/spatialmath/geom2d.py
+++ b/spatialmath/geom2d.py
@@ -9,10 +9,10 @@
 
 from functools import reduce
 import warnings
-import matplotlib.pyplot as plt
-from matplotlib.path import Path
-from matplotlib.patches import PathPatch
-from matplotlib.transforms import Affine2D
+import matplotlib.pyplot as plt # type: ignore
+from matplotlib.path import Path # type: ignore
+from matplotlib.patches import PathPatch # type: ignore
+from matplotlib.transforms import Affine2D # type: ignore
 import numpy as np
 
 from spatialmath import SE2
diff --git a/spatialmath/geom3d.py b/spatialmath/geom3d.py
index 8b191ebd..a109861c 100755
--- a/spatialmath/geom3d.py
+++ b/spatialmath/geom3d.py
@@ -6,7 +6,7 @@
 import numpy as np
 import math
 from collections import namedtuple
-import matplotlib.pyplot as plt
+import matplotlib.pyplot as plt # type: ignore
 import spatialmath.base as base
 from spatialmath.base.types import *
 from spatialmath.baseposelist import BasePoseList
@@ -714,7 +714,7 @@ def isintersecting(
         """
         return not l1.isparallel(l2, tol=tol) and bool(abs(l1 * l2) < tol * _eps)
 
-    def __eq__(l1, l2: Line3) -> bool:  # type: ignore pylint: disable=no-self-argument
+    def __eq__(l1, l2: Line3) -> bool:  # type: ignore # pylint: disable=no-self-argument
         """
         Test if two lines are equivalent
 
@@ -733,7 +733,7 @@ def __eq__(l1, l2: Line3) -> bool:  # type: ignore pylint: disable=no-self-argum
         """
         return l1.isequal(l2)
 
-    def __ne__(l1, l2: Line3) -> bool:  # type:ignore pylint: disable=no-self-argument
+    def __ne__(l1, l2: Line3) -> bool:  # type:ignore # pylint: disable=no-self-argument
         """
         Test if two lines are not equivalent
 
@@ -752,7 +752,7 @@ def __ne__(l1, l2: Line3) -> bool:  # type:ignore pylint: disable=no-self-argume
         """
         return not l1.isequal(l2)
 
-    def __or__(l1, l2: Line3) -> bool:  # type:ignore pylint: disable=no-self-argument
+    def __or__(l1, l2: Line3) -> bool:  # type:ignore # pylint: disable=no-self-argument
         """
         Overloaded ``|`` operator tests for parallelism
 
@@ -771,7 +771,7 @@ def __or__(l1, l2: Line3) -> bool:  # type:ignore pylint: disable=no-self-argume
         """
         return l1.isparallel(l2)
 
-    def __xor__(l1, l2: Line3) -> bool:  # type:ignore pylint: disable=no-self-argument
+    def __xor__(l1, l2: Line3) -> bool:  # type:ignore # pylint: disable=no-self-argument
         """
         Overloaded ``^`` operator tests for intersection
 
@@ -989,7 +989,7 @@ def closest_to_point(self, x: ArrayLike3) -> Tuple[R3, float]:
 
     def commonperp(
         l1, l2: Line3
-    ) -> Line3:  # type:ignore pylint: disable=no-self-argument
+    ) -> Line3:  # type:ignore # pylint: disable=no-self-argument
         """
         Common perpendicular to two lines
 
@@ -1019,7 +1019,7 @@ def commonperp(
 
     def __mul__(
         left, right: Line3
-    ) -> float:  # type:ignore pylint: disable=no-self-argument
+    ) -> float:  # type:ignore # pylint: disable=no-self-argument
         r"""
         Reciprocal product
 
@@ -1047,7 +1047,7 @@ def __mul__(
 
     def __rmul__(
         right, left: SE3
-    ) -> Line3:  # type:ignore pylint: disable=no-self-argument
+    ) -> Line3:  # type:ignore # pylint: disable=no-self-argument
         """
         Rigid-body transformation of 3D line
 
diff --git a/spatialmath/pose3d.py b/spatialmath/pose3d.py
index b4301d93..beb79526 100644
--- a/spatialmath/pose3d.py
+++ b/spatialmath/pose3d.py
@@ -53,31 +53,12 @@ class SO3(BasePoseMatrix):
        :parts: 1
     """
 
-    @overload
-    def __init__(self):
-        ...
-
-    @overload
-    def __init__(self, arg: SO3, *, check=True):
-        ...
-
-    @overload
-    def __init__(self, arg: SE3, *, check=True):
-        ...
-
-    @overload
-    def __init__(self, arg: SO3Array, *, check=True):
-        ...
-
-    @overload
-    def __init__(self, arg: List[SO3Array], *, check=True):
-        ...
-
-    @overload
-    def __init__(self, arg: List[Union[SO3, SO3Array]], *, check=True):
-        ...
-
-    def __init__(self, arg=None, *, check=True):
+    def __init__(
+            self,
+            arg : None | SO3 | SE3 | SO3Array | List[SO3 | SO3Array] = None,
+            *,
+            check=True,
+    ):
         """
         Construct new SO(3) object
 
@@ -483,6 +464,11 @@ def Rand(cls, N: int = 1, *, theta_range:Optional[ArrayLike2] = None, unit: str
         """
         return cls([smb.q2r(smb.qrand(theta_range=theta_range, unit=unit)) for _ in range(0, N)], check=False)
 
+    @overload
+    @classmethod
+    def Eul(cls, phi: float, theta: float, psi: float, unit: str = "rad") -> SE3:
+        ...
+
     @overload
     @classmethod
     def Eul(cls, *angles: float, unit: str = "rad") -> Self:
@@ -533,6 +519,11 @@ def Eul(cls, *angles, unit: str = "rad") -> Self:
         else:
             return cls([smb.eul2r(a, unit=unit) for a in angles], check=False)
 
+    @overload
+    @classmethod
+    def RPY(cls, roll: float, pitch: float, yaw: float, unit: str = "rad") -> SE3:
+        ...
+
     @overload
     @classmethod
     def RPY(
@@ -814,6 +805,8 @@ def Exp(
         r"""
         Create an SO(3) rotation matrix from so(3)
 
+        TODO: clean up typing for S, possibly by introducing additional type parameters at the class level.
+
         :param S: Lie algebra so(3)
         :type S: ndarray(3,3), ndarray(n,3)
         :param check: check that passed matrix is valid so(3), default True
@@ -837,9 +830,9 @@ def Exp(
         :seealso: :func:`spatialmath.base.transforms3d.trexp`, :func:`spatialmath.base.transformsNd.skew`
         """
         if smb.ismatrix(S, (-1, 3)) and not so3:
-            return cls([smb.trexp(s, check=check) for s in S], check=False)
+            return cls([smb.trexp_SO3(s, check=check) for s in S], check=False)
         else:
-            return cls(smb.trexp(cast(R3, S), check=check), check=False)
+            return cls(smb.trexp_SO3(cast(R3, S), check=check), check=False)
 
     def UnitQuaternion(self) -> UnitQuaternion:
         """
@@ -864,7 +857,7 @@ def UnitQuaternion(self) -> UnitQuaternion:
 
         return UnitQuaternion(smb.r2q(self.R), check=False)
 
-    def angdist(self, other: SO3, metric: int = 6) -> Union[float, ndarray]:
+    def angdist(self, other: Self, metric: int = 6) -> Union[float, ndarray]:
         r"""
         Angular distance metric between rotations
 
@@ -1574,10 +1567,12 @@ def Rand(
         )
 
     @overload
+    @classmethod
     def Eul(cls, phi: float, theta: float, psi: float, unit: str = "rad") -> SE3:
         ...
 
     @overload
+    @classmethod
     def Eul(cls, angles: ArrayLike3, unit: str = "rad") -> SE3:
         ...
 
@@ -1624,10 +1619,12 @@ def Eul(cls, *angles, unit="rad") -> SE3:
             return cls([smb.eul2tr(a, unit=unit) for a in angles], check=False)
 
     @overload
+    @classmethod
     def RPY(cls, roll: float, pitch: float, yaw: float, unit: str = "rad") -> SE3:
         ...
 
     @overload
+    @classmethod
     def RPY(cls, angles: ArrayLike3, unit: str = "rad") -> SE3:
         ...
 
@@ -1816,6 +1813,8 @@ def Exp(cls, S: Union[R6, R4x4], check: bool = True) -> SE3:
         """
         Create an SE(3) matrix from se(3)
 
+        TODO: clean up typing for S, possibly by introducing additional type parameters at the class level.
+
         :param S: Lie algebra se(3) matrix
         :type S: ndarray(6), ndarray(4,4)
         :return: SE(3) matrix
@@ -1829,9 +1828,9 @@ def Exp(cls, S: Union[R6, R4x4], check: bool = True) -> SE3:
         :seealso: :func:`~spatialmath.base.transforms3d.trexp`, :func:`~spatialmath.base.transformsNd.skew`
         """
         if smb.isvector(S, 6):
-            return cls(smb.trexp(smb.getvector(S)), check=False)
+            return cls(smb.trexp_SE3(smb.getvector(S)), check=False)
         else:
-            return cls(smb.trexp(S), check=False)
+            return cls(smb.trexp_SE3(S), check=False)
 
     @classmethod
     def Delta(cls, d: ArrayLike6) -> SE3:
@@ -1854,10 +1853,12 @@ def Delta(cls, d: ArrayLike6) -> SE3:
         return cls(smb.trnorm(smb.delta2tr(d)))
 
     @overload
+    @classmethod
     def Trans(cls, x: float, y: float, z: float) -> SE3:
         ...
 
     @overload
+    @classmethod
     def Trans(cls, xyz: ArrayLike3) -> SE3:
         ...
 
@@ -2020,7 +2021,7 @@ def CopyFrom(
             raise ValueError("Transformation matrix must not be None")
         return cls(np.copy(T), check=check)
 
-    def angdist(self, other: SE3, metric: int = 6) -> float:
+    def angdist(self, other: Self, metric: int = 6) -> float:
         r"""
         Angular distance metric between poses
 
diff --git a/spatialmath/quaternion.py b/spatialmath/quaternion.py
index 51561036..0b458dab 100644
--- a/spatialmath/quaternion.py
+++ b/spatialmath/quaternion.py
@@ -131,7 +131,7 @@ def shape(self) -> Tuple[int]:
         return (4,)
 
     @staticmethod
-    def isvalid(x: ArrayLike4) -> bool:
+    def isvalid(x, check: bool=True):
         """
         Test if vector is valid quaternion
 
@@ -473,7 +473,7 @@ def inner(self, other) -> float:
     # -------------------------------------------- operators
 
     def __eq__(
-        left, right: Quaternion
+        left, right
     ) -> bool:  # lgtm[py/not-named-self] pylint: disable=no-self-argument
         """
         Overloaded ``==`` operator
@@ -501,7 +501,7 @@ def __eq__(
         return left.binop(right, smb.qisequal, list1=False)
 
     def __ne__(
-        left, right: Quaternion
+        left, right
     ) -> bool:  # lgtm[py/not-named-self] pylint: disable=no-self-argument
         """
         Overloaded ``!=`` operator
@@ -528,7 +528,7 @@ def __ne__(
         return left.binop(right, lambda x, y: not smb.qisequal(x, y), list1=False)
 
     def __mul__(
-        left, right: Quaternion
+        left, right
     ) -> Quaternion:  # lgtm[py/not-named-self] pylint: disable=no-self-argument
         """
         Overloaded ``*`` operator
@@ -591,7 +591,7 @@ def __mul__(
             raise ValueError("operands to * are of different types")
 
     def __rmul__(
-        right, left: Quaternion
+        right, left
     ) -> Quaternion:  # lgtm[py/not-named-self] pylint: disable=no-self-argument
         """
         Overloaded ``*`` operator
@@ -616,8 +616,8 @@ def __rmul__(
         return Quaternion([left * q._A for q in right])
 
     def __imul__(
-        left, right: Quaternion
-    ) -> bool:  # lgtm[py/not-named-self] pylint: disable=no-self-argument
+        left, right
+    ):  # lgtm[py/not-named-self] pylint: disable=no-self-argument
         """
         Overloaded ``*=`` operator
 
@@ -1570,7 +1570,7 @@ def dotb(self, omega: ArrayLike3) -> R4:
         return smb.qdotb(self._A, omega)
 
     def __mul__(
-        left, right: UnitQuaternion
+        left, right
     ) -> UnitQuaternion:  # lgtm[py/not-named-self] pylint: disable=no-self-argument
         """
         Multiply unit quaternion
@@ -1668,7 +1668,7 @@ def __mul__(
             raise ValueError("UnitQuaternion: operands to * are of different types")
 
     def __imul__(
-        left, right: UnitQuaternion
+        left, right
     ) -> UnitQuaternion:  # lgtm[py/not-named-self] pylint: disable=no-self-argument
         """
         Multiply unit quaternion in place
@@ -1692,7 +1692,7 @@ def __imul__(
         return left.__mul__(right)
 
     def __truediv__(
-        left, right: UnitQuaternion
+        left, right
     ) -> UnitQuaternion:  # lgtm[py/not-named-self] pylint: disable=no-self-argument
         """
         Overloaded ``/`` operator
@@ -1756,7 +1756,7 @@ def __truediv__(
             raise ValueError("bad operands")
 
     def __eq__(
-        left, right: UnitQuaternion
+        left, right
     ) -> bool:  # lgtm[py/not-named-self] pylint: disable=no-self-argument
         """
         Overloaded ``==`` operator
@@ -1787,7 +1787,7 @@ def __eq__(
         )
 
     def __ne__(
-        left, right: UnitQuaternion
+        left, right
     ) -> bool:  # lgtm[py/not-named-self] pylint: disable=no-self-argument
         """
         Overloaded ``!=`` operator
@@ -1818,7 +1818,7 @@ def __ne__(
         )
 
     def __matmul__(
-        left, right: UnitQuaternion
+        left, right
     ) -> UnitQuaternion:  # lgtm[py/not-named-self] pylint: disable=no-self-argument
         """
         Overloaded @ operator
diff --git a/spatialmath/spline.py b/spatialmath/spline.py
index 0a472ecc..c19ec2b2 100644
--- a/spatialmath/spline.py
+++ b/spatialmath/spline.py
@@ -9,10 +9,10 @@
 from functools import cached_property
 from typing import List, Optional, Tuple, Set
 
-import matplotlib.pyplot as plt
+import matplotlib.pyplot as plt # type: ignore
 import numpy as np
-from scipy.interpolate import BSpline, CubicSpline
-from scipy.spatial.transform import Rotation, RotationSpline
+from scipy.interpolate import BSpline, CubicSpline # type: ignore
+from scipy.spatial.transform import Rotation, RotationSpline # type: ignore
 
 from spatialmath import SE3, SO3, Twist3
 from spatialmath.base.transforms3d import tranimate
@@ -20,7 +20,7 @@
 
 class SplineSE3(ABC):
     def __init__(self) -> None:
-        self.control_poses: SE3
+        self.control_poses: List[SE3]
 
     @abstractmethod
     def __call__(self, t: float) -> SE3:
diff --git a/spatialmath/timing.py b/spatialmath/timing.py
index ae169909..82e96c9d 100755
--- a/spatialmath/timing.py
+++ b/spatialmath/timing.py
@@ -8,7 +8,7 @@
 
 
 import timeit
-from ansitable import ANSITable, Column
+from ansitable import ANSITable, Column # type: ignore
 
 N = 100000
 
diff --git a/spatialmath/twist.py b/spatialmath/twist.py
index f84a0f1b..1a30a8e6 100644
--- a/spatialmath/twist.py
+++ b/spatialmath/twist.py
@@ -916,9 +916,9 @@ def skewa(self):
             >>> smb.trexp(se)
         """
         if len(self) == 1:
-            return smb.skewa(self.S)
+            return smb.skewa3(self.S)
         else:
-            return [smb.skewa(x.S) for x in self]
+            return [smb.skewa3(x.S) for x in self]
 
     @property
     def pitch(self):
@@ -1015,13 +1015,13 @@ def SE3(self, theta=1, unit="rad"):
 
         if len(theta) == 1:
             # theta is a scalar
-            return SE3(smb.trexp(self.S * theta))
+            return SE3(smb.trexp_SE3(self.S * theta))
         else:
             # theta is a vector
             if len(self) == 1:
-                return SE3([smb.trexp(self.S * t) for t in theta])
+                return SE3([smb.trexp_SE3(self.S * t) for t in theta])
             elif len(self) == len(theta):
-                return SE3([smb.trexp(S * t) for S, t in zip(self.data, theta)])
+                return SE3([smb.trexp_SE3(S * t) for S, t in zip(self.data, theta)])
             else:
                 raise ValueError("length of twist and theta not consistent")
 
@@ -1072,9 +1072,9 @@ def exp(self, theta=1, unit="rad"):
         theta = smb.getunit(theta, unit)
 
         if len(self) == 1:
-            return SE3([smb.trexp(self.S * t) for t in theta], check=False)
+            return SE3([smb.trexp_SE3(self.S * t) for t in theta], check=False)
         elif len(self) == len(theta):
-            return SE3([smb.trexp(s * t) for s, t in zip(self.S, theta)], check=False)
+            return SE3([smb.trexp_SE3(s * t) for s, t in zip(self.S, theta)], check=False)
         else:
             raise ValueError("length mismatch")
 
@@ -1136,12 +1136,12 @@ def __mul__(
             return Twist3(
                 left.binop(
                     right,
-                    lambda x, y: smb.trlog(smb.trexp(x) @ smb.trexp(y), twist=True),
+                    lambda x, y: smb.trlog(smb.trexp_SE3(x) @ smb.trexp_SE3(y), twist=True),
                 )
             )
         elif isinstance(right, SE3):
             # twist * SE3 -> SE3
-            return SE3(left.binop(right, lambda x, y: smb.trexp(x) @ y), check=False)
+            return SE3(left.binop(right, lambda x, y: smb.trexp_SE3(x) @ y), check=False)
         elif smb.isscalar(right):
             # return Twist(left.S * right)
             return Twist3(left.binop(right, lambda x, y: x * y))
@@ -1558,9 +1558,9 @@ def skewa(self):
             >>> smb.trexp2(se)
         """
         if len(self) == 1:
-            return smb.skewa(self.S)
+            return smb.skewa2(self.S)
         else:
-            return [smb.skewa(x.S) for x in self]
+            return [smb.skewa2(x.S) for x in self]
 
     def exp(self, theta=1, unit="rad"):
         r"""
diff --git a/tests/base/test_transformsNd.py b/tests/base/test_transformsNd.py
index 92d9e2a3..4568e46f 100755
--- a/tests/base/test_transformsNd.py
+++ b/tests/base/test_transformsNd.py
@@ -361,23 +361,35 @@ def test_isskewa(self):
         sk[2, 2] = 3
         self.assertFalse(isskew(sk))
 
-    def test_skewa(self):
+    def test_skewa3(self):
         # 3D
-        sk = skewa([1, 2, 3, 4, 5, 6])
+        sk = skewa3([1, 2, 3, 4, 5, 6])
         self.assertEqual(sk.shape, (4, 4))
         nt.assert_almost_equal(sk.diagonal(), np.r_[0, 0, 0, 0])
         nt.assert_almost_equal(sk[-1, :], np.r_[0, 0, 0, 0])
         nt.assert_almost_equal(sk[:3, 3], [1, 2, 3])
         nt.assert_almost_equal(vex(sk[:3, :3]), [4, 5, 6])
 
+    def test_skewa2(self):
         # 2D
-        sk = skewa([1, 2, 3])
+        sk = skewa2([1, 2, 3])
         self.assertEqual(sk.shape, (3, 3))
         nt.assert_almost_equal(sk.diagonal(), np.r_[0, 0, 0])
         nt.assert_almost_equal(sk[-1, :], np.r_[0, 0, 0])
         nt.assert_almost_equal(sk[:2, 2], [1, 2])
         nt.assert_almost_equal(vex(sk[:2, :2]), [3])
 
+    def test_skewa_skewa3(self):
+        # 3D
+        v = [1, 2, 3, 4, 5, 6]
+        nt.assert_equal(skewa(v), skewa3(v))
+
+    def test_skewa_skewa2(self):
+        # 2D
+        v = [1, 2, 3]
+        nt.assert_equal(skewa(v), skewa2(v))
+
+    def test_skew_raises(self):
         with self.assertRaises(ValueError):
             sk = skew([1, 2])
 

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