diff --git a/CHANGELOG.md b/CHANGELOG.md
index 3944d22c2b..abdd7ca512 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -20,6 +20,9 @@ The format is based on [Keep a Changelog](https://keepachangelog.com/en/1.0.0/).
 - Add ``collision_color`` parameter to `MeshcatVisualizer.loadViewerModel` ([#2350](https://github.com/stack-of-tasks/pinocchio/pull/2350))
 - Add ``BuildFromMJCF`` function to RobotWrapper ([#2363](https://github.com/stack-of-tasks/pinocchio/pull/2363))
 
+### Removed
+- Remove deprecated headers related to joint constraints ([#2382](https://github.com/stack-of-tasks/pinocchio/pull/2382))
+
 ### Changed
 - Use eigenpy to expose `GeometryObject::meshMaterial` variant ([#2315](https://github.com/stack-of-tasks/pinocchio/pull/2315))
 - GepettoViewer is no more the default viewer for RobotWrapper ([#2331](https://github.com/stack-of-tasks/pinocchio/pull/2331))
diff --git a/cmake b/cmake
index 91b8f5f216..b3c2af1b68 160000
--- a/cmake
+++ b/cmake
@@ -1 +1 @@
-Subproject commit 91b8f5f2168b123a198da079b8e6c09fd1f60285
+Subproject commit b3c2af1b68686dc9d5f459fb617647e37a15a76d
diff --git a/include/pinocchio/multibody/constraint-base.hpp b/include/pinocchio/multibody/constraint-base.hpp
deleted file mode 100644
index ea9880cb20..0000000000
--- a/include/pinocchio/multibody/constraint-base.hpp
+++ /dev/null
@@ -1,202 +0,0 @@
-//
-// Copyright (c) 2015-2020 CNRS INRIA
-// Copyright (c) 2016 Wandercraft, 86 rue de Paris 91400 Orsay, France.
-//
-
-#ifndef __pinocchio_multibody_constraint_base_hpp__
-#define __pinocchio_multibody_constraint_base_hpp__
-
-#include "pinocchio/macros.hpp"
-#include "pinocchio/spatial/fwd.hpp"
-#include "pinocchio/spatial/motion.hpp"
-#include "pinocchio/spatial/act-on-set.hpp"
-
-#include <boost/static_assert.hpp>
-
-// S   : v   \in M^6              -> v_J \in lie(Q) ~= R^nv
-// S^T : f_J \in lie(Q)^* ~= R^nv -> f    \in F^6
-
-#define PINOCCHIO_CONSTRAINT_TYPEDEF_GENERIC(DERIVED, TYPENAME)                                    \
-  typedef TYPENAME traits<DERIVED>::Scalar Scalar;                                                 \
-  typedef TYPENAME traits<DERIVED>::JointMotion JointMotion;                                       \
-  typedef TYPENAME traits<DERIVED>::JointForce JointForce;                                         \
-  typedef TYPENAME traits<DERIVED>::DenseBase DenseBase;                                           \
-  typedef TYPENAME traits<DERIVED>::MatrixReturnType MatrixReturnType;                             \
-  typedef TYPENAME traits<DERIVED>::ConstMatrixReturnType ConstMatrixReturnType;                   \
-  enum                                                                                             \
-  {                                                                                                \
-    LINEAR = traits<DERIVED>::LINEAR,                                                              \
-    ANGULAR = traits<DERIVED>::ANGULAR                                                             \
-  };                                                                                               \
-  enum                                                                                             \
-  {                                                                                                \
-    Options = traits<DERIVED>::Options                                                             \
-  };
-
-#define PINOCCHIO_CONSTRAINT_TYPEDEF_TPL(DERIVED)                                                  \
-  PINOCCHIO_CONSTRAINT_TYPEDEF_GENERIC(DERIVED, typename)
-#define PINOCCHIO_CONSTRAINT_TYPEDEF(DERIVED)                                                      \
-  PINOCCHIO_CONSTRAINT_TYPEDEF_GENERIC(DERIVED, PINOCCHIO_EMPTY_ARG)
-
-namespace pinocchio
-{
-
-  /// \brief Return type of the Constraint::Transpose * Force operation
-  template<class ConstraintDerived, typename Force>
-  struct ConstraintForceOp
-  {
-    typedef ReturnTypeNotDefined ReturnType;
-  };
-
-  /// \brief Return type of the Constraint::Transpose * ForceSet operation
-  template<class ConstraintDerived, typename ForceSet>
-  struct ConstraintForceSetOp
-  {
-    typedef ReturnTypeNotDefined ReturnType;
-  };
-
-  template<class Derived>
-  class JointMotionSubspaceBase : public NumericalBase<Derived>
-  {
-  protected:
-    PINOCCHIO_CONSTRAINT_TYPEDEF_TPL(Derived)
-
-  public:
-    EIGEN_MAKE_ALIGNED_OPERATOR_NEW
-
-    Derived & derived()
-    {
-      return *static_cast<Derived *>(this);
-    }
-    const Derived & derived() const
-    {
-      return *static_cast<const Derived *>(this);
-    }
-
-    template<typename VectorLike>
-    JointMotion operator*(const Eigen::MatrixBase<VectorLike> & vj) const
-    {
-      return derived().__mult__(vj);
-    }
-
-    MatrixReturnType matrix()
-    {
-      return derived().matrix_impl();
-    }
-    ConstMatrixReturnType matrix() const
-    {
-      return derived().matrix_impl();
-    }
-
-    int nv() const
-    {
-      return derived().nv_impl();
-    }
-
-    static int rows()
-    {
-      return 6;
-    }
-    int cols() const
-    {
-      return nv();
-    }
-
-    template<class OtherDerived>
-    bool isApprox(
-      const JointMotionSubspaceBase<OtherDerived> & other,
-      const Scalar & prec = Eigen::NumTraits<Scalar>::dummy_precision()) const
-    {
-      return matrix().isApprox(other.matrix(), prec);
-    }
-
-    void disp(std::ostream & os) const
-    {
-      derived().disp_impl(os);
-    }
-    friend std::ostream & operator<<(std::ostream & os, const JointMotionSubspaceBase<Derived> & X)
-    {
-      X.disp(os);
-      return os;
-    }
-
-    typename SE3GroupAction<Derived>::ReturnType se3Action(const SE3Tpl<Scalar, Options> & m) const
-    {
-      return derived().se3Action(m);
-    }
-
-    typename SE3GroupAction<Derived>::ReturnType
-    se3ActionInverse(const SE3Tpl<Scalar, Options> & m) const
-    {
-      return derived().se3ActionInverse(m);
-    }
-
-    template<typename MotionDerived>
-    typename MotionAlgebraAction<Derived, MotionDerived>::ReturnType
-    motionAction(const MotionDense<MotionDerived> & v) const
-    {
-      return derived().motionAction(v);
-    }
-
-    bool operator==(const JointMotionSubspaceBase<Derived> & other) const
-    {
-      return derived().isEqual(other.derived());
-    }
-
-  }; // class JointMotionSubspaceBase
-
-  ///  \brief Operation Y * S used in the CRBA algorithm for instance
-  template<typename Scalar, int Options, typename ConstraintDerived>
-  typename MultiplicationOp<InertiaTpl<Scalar, Options>, ConstraintDerived>::ReturnType operator*(
-    const InertiaTpl<Scalar, Options> & Y,
-    const JointMotionSubspaceBase<ConstraintDerived> & constraint)
-  {
-    return impl::LhsMultiplicationOp<InertiaTpl<Scalar, Options>, ConstraintDerived>::run(
-      Y, constraint.derived());
-  }
-
-  ///  \brief Operation Y_matrix * S used in the ABA algorithm for instance
-  template<typename MatrixDerived, typename ConstraintDerived>
-  typename MultiplicationOp<Eigen::MatrixBase<MatrixDerived>, ConstraintDerived>::ReturnType
-  operator*(
-    const Eigen::MatrixBase<MatrixDerived> & Y,
-    const JointMotionSubspaceBase<ConstraintDerived> & constraint)
-  {
-    return impl::LhsMultiplicationOp<Eigen::MatrixBase<MatrixDerived>, ConstraintDerived>::run(
-      Y.derived(), constraint.derived());
-  }
-
-  namespace details
-  {
-    template<typename Constraint>
-    struct StDiagonalMatrixSOperation
-    {
-      typedef typename traits<Constraint>::StDiagonalMatrixSOperationReturnType ReturnType;
-      typedef typename traits<Constraint>::ReducedSquaredMatrix ReducedSquaredMatrix;
-
-      static ReturnType run(const JointMotionSubspaceBase<Constraint> & /*constraint*/)
-      {
-        return ReducedSquaredMatrix::Identity(Constraint::NV, Constraint::NV);
-      }
-    };
-  } // namespace details
-
-  template<class ConstraintDerived>
-  struct JointMotionSubspaceTransposeBase
-  {
-    typedef typename traits<ConstraintDerived>::StDiagonalMatrixSOperationReturnType
-      StDiagonalMatrixSOperationReturnType;
-  };
-
-  template<class ConstraintDerived>
-  typename JointMotionSubspaceTransposeBase<ConstraintDerived>::StDiagonalMatrixSOperationReturnType
-  operator*(
-    const JointMotionSubspaceTransposeBase<ConstraintDerived> & /*S_transpose*/,
-    const JointMotionSubspaceBase<ConstraintDerived> & S)
-  {
-    return details::StDiagonalMatrixSOperation<ConstraintDerived>::run(S.derived());
-  }
-
-} // namespace pinocchio
-
-#endif // ifndef __pinocchio_multibody_constraint_base_hpp__
diff --git a/include/pinocchio/multibody/constraint-generic.hpp b/include/pinocchio/multibody/constraint-generic.hpp
deleted file mode 100644
index 7ef1026b50..0000000000
--- a/include/pinocchio/multibody/constraint-generic.hpp
+++ /dev/null
@@ -1,212 +0,0 @@
-//
-// Copyright (c) 2015-2020 CNRS INRIA
-// Copyright (c) 2016 Wandercraft, 86 rue de Paris 91400 Orsay, France.
-//
-
-#ifndef __pinocchio_multibody_constraint_generic_hpp__
-#define __pinocchio_multibody_constraint_generic_hpp__
-
-namespace pinocchio
-{
-
-  template<int _Dim, typename _Scalar, int _Options>
-  struct traits<JointMotionSubspaceTpl<_Dim, _Scalar, _Options>>
-  {
-    typedef _Scalar Scalar;
-    enum
-    {
-      LINEAR = 0,
-      ANGULAR = 3,
-      Options = _Options,
-      Dim = _Dim
-    };
-
-    typedef MotionTpl<Scalar, Options> JointMotion;
-    typedef Eigen::Matrix<Scalar, Dim, 1, Options> JointForce;
-    typedef Eigen::Matrix<Scalar, 6, Dim, Options> DenseBase;
-    typedef Eigen::Matrix<Scalar, Dim, Dim, Options> ReducedSquaredMatrix;
-
-    typedef typename PINOCCHIO_EIGEN_REF_CONST_TYPE(DenseBase) ConstMatrixReturnType;
-    typedef typename PINOCCHIO_EIGEN_REF_TYPE(DenseBase) MatrixReturnType;
-
-    typedef ReducedSquaredMatrix StDiagonalMatrixSOperationReturnType;
-  }; // traits JointMotionSubspaceTpl
-
-  template<int Dim, typename Scalar, int Options>
-  struct SE3GroupAction<JointMotionSubspaceTpl<Dim, Scalar, Options>>
-  {
-    typedef Eigen::Matrix<Scalar, 6, Dim> ReturnType;
-  };
-
-  template<int Dim, typename Scalar, int Options, typename MotionDerived>
-  struct MotionAlgebraAction<JointMotionSubspaceTpl<Dim, Scalar, Options>, MotionDerived>
-  {
-    typedef Eigen::Matrix<Scalar, 6, Dim> ReturnType;
-  };
-
-  template<int _Dim, typename _Scalar, int _Options>
-  struct JointMotionSubspaceTpl
-  : public JointMotionSubspaceBase<JointMotionSubspaceTpl<_Dim, _Scalar, _Options>>
-  {
-    EIGEN_MAKE_ALIGNED_OPERATOR_NEW
-
-    typedef JointMotionSubspaceBase<JointMotionSubspaceTpl> Base;
-
-    friend class JointMotionSubspaceBase<JointMotionSubspaceTpl>;
-    PINOCCHIO_CONSTRAINT_TYPEDEF_TPL(JointMotionSubspaceTpl)
-
-    enum
-    {
-      NV = _Dim
-    };
-
-    using Base::nv;
-
-    template<typename D>
-    explicit JointMotionSubspaceTpl(const Eigen::MatrixBase<D> & _S)
-    : S(_S)
-    {
-      // There is currently a bug in Eigen/Core/util/StaticAssert.h in the use of the full namespace
-      // path
-      // TODO
-      EIGEN_STATIC_ASSERT_SAME_MATRIX_SIZE(DenseBase, D);
-    }
-
-    JointMotionSubspaceTpl()
-    : S()
-    {
-      EIGEN_STATIC_ASSERT(
-        _Dim != Eigen::Dynamic, YOU_CALLED_A_DYNAMIC_SIZE_METHOD_ON_A_FIXED_SIZE_MATRIX_OR_VECTOR)
-    }
-
-    // It is only valid for dynamics size
-    explicit JointMotionSubspaceTpl(const int dim)
-    : S(6, dim)
-    {
-      EIGEN_STATIC_ASSERT(
-        _Dim == Eigen::Dynamic, YOU_CALLED_A_FIXED_SIZE_METHOD_ON_A_DYNAMIC_SIZE_MATRIX_OR_VECTOR)
-    }
-
-    static JointMotionSubspaceTpl Zero(const int dim)
-    {
-      return JointMotionSubspaceTpl(dim);
-    }
-
-    template<typename VectorLike>
-    JointMotion __mult__(const Eigen::MatrixBase<VectorLike> & vj) const
-    {
-      return JointMotion(S * vj);
-    }
-
-    struct Transpose : JointMotionSubspaceTransposeBase<JointMotionSubspaceTpl>
-    {
-      const JointMotionSubspaceTpl & ref;
-      Transpose(const JointMotionSubspaceTpl & ref)
-      : ref(ref)
-      {
-      }
-
-      template<typename Derived>
-      JointForce operator*(const ForceDense<Derived> & f) const
-      {
-        return (ref.S.transpose() * f.toVector()).eval();
-      }
-
-      template<typename D>
-      typename Eigen::Matrix<Scalar, NV, Eigen::Dynamic> operator*(const Eigen::MatrixBase<D> & F)
-      {
-        return (ref.S.transpose() * F).eval();
-      }
-    };
-
-    Transpose transpose() const
-    {
-      return Transpose(*this);
-    }
-
-    MatrixReturnType matrix_impl()
-    {
-      return S;
-    }
-    ConstMatrixReturnType matrix_impl() const
-    {
-      return S;
-    }
-
-    int nv_impl() const
-    {
-      return (int)S.cols();
-    }
-
-    template<typename S2, int O2>
-    friend typename JointMotionSubspaceTpl<_Dim, _Scalar, _Options>::DenseBase
-    operator*(const InertiaTpl<S2, O2> & Y, const JointMotionSubspaceTpl & S)
-    {
-      typedef typename JointMotionSubspaceTpl::DenseBase ReturnType;
-      ReturnType res(6, S.nv());
-      motionSet::inertiaAction(Y, S.S, res);
-      return res;
-    }
-
-    template<typename S2, int O2>
-    friend Eigen::Matrix<_Scalar, 6, _Dim>
-    operator*(const Eigen::Matrix<S2, 6, 6, O2> & Ymatrix, const JointMotionSubspaceTpl & S)
-    {
-      typedef Eigen::Matrix<_Scalar, 6, _Dim> ReturnType;
-      return ReturnType(Ymatrix * S.matrix());
-    }
-
-    DenseBase se3Action(const SE3Tpl<Scalar, Options> & m) const
-    {
-      DenseBase res(6, nv());
-      motionSet::se3Action(m, S, res);
-      return res;
-    }
-
-    DenseBase se3ActionInverse(const SE3Tpl<Scalar, Options> & m) const
-    {
-      DenseBase res(6, nv());
-      motionSet::se3ActionInverse(m, S, res);
-      return res;
-    }
-
-    template<typename MotionDerived>
-    DenseBase motionAction(const MotionDense<MotionDerived> & v) const
-    {
-      DenseBase res(6, nv());
-      motionSet::motionAction(v, S, res);
-      return res;
-    }
-
-    void disp_impl(std::ostream & os) const
-    {
-      os << "S =\n" << S << std::endl;
-    }
-
-    bool isEqual(const JointMotionSubspaceTpl & other) const
-    {
-      return S == other.S;
-    }
-
-  protected:
-    DenseBase S;
-  }; // class JointMotionSubspaceTpl
-
-  namespace details
-  {
-    template<int Dim, typename Scalar, int Options>
-    struct StDiagonalMatrixSOperation<JointMotionSubspaceTpl<Dim, Scalar, Options>>
-    {
-      typedef JointMotionSubspaceTpl<Dim, Scalar, Options> Constraint;
-      typedef typename traits<Constraint>::StDiagonalMatrixSOperationReturnType ReturnType;
-
-      static ReturnType run(const JointMotionSubspaceBase<Constraint> & constraint)
-      {
-        return constraint.matrix().transpose() * constraint.matrix();
-      }
-    };
-  } // namespace details
-
-} // namespace pinocchio
-
-#endif // ifndef __pinocchio_multibody_constraint_generic_hpp__
diff --git a/include/pinocchio/serialization/joints-constraint.hpp b/include/pinocchio/serialization/joints-constraint.hpp
deleted file mode 100644
index 46a3571be1..0000000000
--- a/include/pinocchio/serialization/joints-constraint.hpp
+++ /dev/null
@@ -1,143 +0,0 @@
-//
-// Copyright (c) 2019-2020 INRIA
-//
-
-#ifndef __pinocchio_serialization_joints_motion_subspace_hpp__
-#define __pinocchio_serialization_joints_motion_subspace_hpp__
-
-#include "pinocchio/serialization/fwd.hpp"
-
-#include <boost/serialization/split_free.hpp>
-#include <boost/serialization/vector.hpp>
-
-namespace boost
-{
-  namespace serialization
-  {
-
-    template<class Archive, typename Scalar, int Options, int axis>
-    void serialize(
-      Archive & /*ar*/,
-      pinocchio::JointMotionSubspaceRevoluteTpl<Scalar, Options, axis> & /*S*/,
-      const unsigned int /*version*/)
-    {
-    }
-
-    template<class Archive, typename Scalar, int Options, int axis>
-    void serialize(
-      Archive & /*ar*/,
-      pinocchio::JointMotionSubspacePrismaticTpl<Scalar, Options, axis> & /*S*/,
-      const unsigned int /*version*/)
-    {
-    }
-
-    template<class Archive, typename Scalar, int Options, int axis>
-    void serialize(
-      Archive & ar,
-      pinocchio::JointMotionSubspaceHelicalTpl<Scalar, Options, axis> & S,
-      const unsigned int /*version*/)
-    {
-      ar & make_nvp("h", S.h());
-    }
-
-    template<class Archive, typename Scalar, int Options>
-    void serialize(
-      Archive & /*ar*/,
-      pinocchio::JointMotionSubspaceSphericalTpl<Scalar, Options> & /*S*/,
-      const unsigned int /*version*/)
-    {
-    }
-
-    template<class Archive, typename Scalar, int Options>
-    void serialize(
-      Archive & /*ar*/,
-      pinocchio::JointMotionSubspaceTranslationTpl<Scalar, Options> & /*S*/,
-      const unsigned int /*version*/)
-    {
-    }
-
-    template<class Archive, typename Scalar, int Options>
-    void serialize(
-      Archive & /*ar*/,
-      pinocchio::JointMotionSubspaceIdentityTpl<Scalar, Options> & /*S*/,
-      const unsigned int /*version*/)
-    {
-    }
-
-    template<class Archive, typename Scalar, int Options>
-    void serialize(
-      Archive & ar,
-      pinocchio::JointMotionSubspaceRevoluteUnalignedTpl<Scalar, Options> & S,
-      const unsigned int /*version*/)
-    {
-      ar & make_nvp("axis", S.axis());
-    }
-
-    template<class Archive, typename Scalar, int Options>
-    void serialize(
-      Archive & ar,
-      pinocchio::JointMotionSubspacePrismaticUnalignedTpl<Scalar, Options> & S,
-      const unsigned int /*version*/)
-    {
-      ar & make_nvp("axis", S.axis());
-    }
-
-    template<class Archive, typename Scalar, int Options>
-    void serialize(
-      Archive & ar,
-      pinocchio::JointMotionSubspaceHelicalUnalignedTpl<Scalar, Options> & S,
-      const unsigned int /*version*/)
-    {
-      ar & make_nvp("axis", S.axis());
-      ar & make_nvp("h", S.h());
-    }
-
-    template<class Archive, typename Scalar, int Options>
-    void serialize(
-      Archive & ar,
-      pinocchio::JointMotionSubspaceUniversalTpl<Scalar, Options> & S,
-      const unsigned int /*version*/)
-    {
-      ar & make_nvp("angularSubspace", S.angularSubspace());
-    }
-
-    template<class Archive, int Dim, typename Scalar, int Options>
-    void serialize(
-      Archive & ar,
-      pinocchio::JointMotionSubspaceTpl<Dim, Scalar, Options> & S,
-      const unsigned int /*version*/)
-    {
-      ar & make_nvp("matrix", S.matrix());
-    }
-
-    template<class Archive, class Constraint>
-    void serialize(
-      Archive & ar,
-      pinocchio::ScaledJointMotionSubspace<Constraint> & S,
-      const unsigned int /*version*/)
-    {
-      ar & make_nvp("scaling", S.scaling());
-      ar & make_nvp("constraint", S.constraint());
-    }
-
-    template<class Archive, typename Scalar, int Options>
-    void serialize(
-      Archive & /*ar*/,
-      pinocchio::JointMotionSubspacePlanarTpl<Scalar, Options> & /*S*/,
-      const unsigned int /*version*/)
-    {
-    }
-
-    template<class Archive, typename Scalar, int Options>
-    void serialize(
-      Archive & ar,
-      pinocchio::JointMotionSubspaceSphericalZYXTpl<Scalar, Options> & S,
-      const unsigned int /*version*/)
-    {
-      ar & make_nvp("angularSubspace", S.angularSubspace());
-    }
-
-  } // namespace serialization
-} // namespace boost
-
-#endif // ifndef __pinocchio_serialization_joints_motion_subspace_hpp__
diff --git a/sources.cmake b/sources.cmake
index 991984996b..dda8d0d52d 100644
--- a/sources.cmake
+++ b/sources.cmake
@@ -153,8 +153,6 @@ set(${PROJECT_NAME}_CORE_PUBLIC_HEADERS
     ${PROJECT_SOURCE_DIR}/include/pinocchio/math/tensor.hpp
     ${PROJECT_SOURCE_DIR}/include/pinocchio/math/triangular-matrix.hpp
     ${PROJECT_SOURCE_DIR}/include/pinocchio/math/tridiagonal-matrix.hpp
-    ${PROJECT_SOURCE_DIR}/include/pinocchio/multibody/constraint-base.hpp
-    ${PROJECT_SOURCE_DIR}/include/pinocchio/multibody/constraint-generic.hpp
     ${PROJECT_SOURCE_DIR}/include/pinocchio/multibody/data.hpp
     ${PROJECT_SOURCE_DIR}/include/pinocchio/multibody/data.hxx
     ${PROJECT_SOURCE_DIR}/include/pinocchio/multibody/fcl.hpp
@@ -236,7 +234,6 @@ set(${PROJECT_NAME}_CORE_PUBLIC_HEADERS
     ${PROJECT_SOURCE_DIR}/include/pinocchio/serialization/fwd.hpp
     ${PROJECT_SOURCE_DIR}/include/pinocchio/serialization/geometry.hpp
     ${PROJECT_SOURCE_DIR}/include/pinocchio/serialization/inertia.hpp
-    ${PROJECT_SOURCE_DIR}/include/pinocchio/serialization/joints-constraint.hpp
     ${PROJECT_SOURCE_DIR}/include/pinocchio/serialization/joints-data.hpp
     ${PROJECT_SOURCE_DIR}/include/pinocchio/serialization/joints.hpp
     ${PROJECT_SOURCE_DIR}/include/pinocchio/serialization/joints-model.hpp