diff --git a/src/mesh/blockMesh/blockEdges/arcEdge/arcEdge.C b/src/mesh/blockMesh/blockEdges/arcEdge/arcEdge.C
index b2f5c57b66..88bb8ebd7d 100644
--- a/src/mesh/blockMesh/blockEdges/arcEdge/arcEdge.C
+++ b/src/mesh/blockMesh/blockEdges/arcEdge/arcEdge.C
@@ -2,7 +2,7 @@
   =========                 |
   \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
    \\    /   O peration     | Website:  https://openfoam.org
-    \\  /    A nd           | Copyright (C) 2011-2018 OpenFOAM Foundation
+    \\  /    A nd           | Copyright (C) 2011-2019 OpenFOAM Foundation
      \\/     M anipulation  |
 -------------------------------------------------------------------------------
 License
@@ -41,87 +41,66 @@ namespace blockEdges
 
 // * * * * * * * * * * * * * Private Member Functions  * * * * * * * * * * * //
 
-Foam::cylindricalCS Foam::blockEdges::arcEdge::calcAngle()
+void Foam::blockEdges::arcEdge::calc(const point& pA)
 {
-    vector a = p2_ - p1_;
-    vector b = p3_ - p1_;
+    const tensor dps(pA - p0_, pA - p1_, (pA - p0_)^(pA - p1_));
+    const tensor pMs((p0_ + pA)/2, (p1_ + pA)/2, pA);
 
-    // find centre of arcEdge
-    scalar asqr = a & a;
-    scalar bsqr = b & b;
-    scalar adotb = a & b;
-
-    scalar denom = asqr*bsqr - adotb*adotb;
-
-    if (mag(denom) < vSmall)
+    if (det(dps) < vSmall)
     {
         FatalErrorInFunction
-            << denom
+            << "Arc point " << pA << " lies on the line of edge "
+            << edge(start_, end_) << abort(FatalError);
+    }
+
+    const point c =
+        inv(dps)
+      & vector(dps.x() & pMs.x(), dps.y() & pMs.y(), dps.z() & pMs.z());
+
+    const vector r0 = p0_ - c, r1 = p1_ - c;
+    const scalar cosT = (r0 & r1)/(mag(r0)*mag(r1));
+    scalar t = acos(max(-1, min(cosT, 1)));
+    if (((r0 ^ r1) & dps.z()) > 0)
+    {
+        t = 2*constant::mathematical::pi - t;
+    }
+
+    centre_ = c;
+    axis_ = - normalised(dps.z());
+    theta_ = t;
+    length_ = 0;
+}
+
+
+void Foam::blockEdges::arcEdge::calc(const scalar theta, const vector& axis)
+{
+    if (0 >= theta || theta >= 360)
+    {
+        FatalErrorInFunction
+            << "Arc angle for edge " << edge(start_, end_)
+            << " must take a value between 0 and 360 degrees"
             << abort(FatalError);
     }
 
-    scalar fact = 0.5*(bsqr - adotb)/denom;
+    const vector dp = p1_ - p0_;
 
-    point centre = 0.5*a + fact*((a ^ b) ^ a);
+    const vector pM = (p0_ + p1_)/2;
+    const vector rM = normalised(dp ^ axis);
 
-    centre += p1_;
+    const scalar l = dp & axis;
 
-    // find position vectors w.r.t. the arcEdge centre
-    vector r1(p1_ - centre);
-    vector r2(p2_ - centre);
-    vector r3(p3_ - centre);
+    const vector chord = dp - l*axis;
+    const scalar magChord = mag(chord);
 
-    // find angles
-    const scalar cosAngle = (r3 & r1)/(mag(r3) * mag(r1));
-    angle_ = radToDeg(acos(max(-1, min(cosAngle, 1))));
-
-    // check if the vectors define an exterior or an interior arcEdge
-    if (((r1 ^ r2) & (r1 ^ r3)) < 0.0)
-    {
-        angle_ = 360.0 - angle_;
-    }
-
-    vector tempAxis;
-
-    if (angle_ <= 180.0)
-    {
-        tempAxis = r1 ^ r3;
-
-        if (mag(tempAxis)/(mag(r1)*mag(r3)) < 0.001)
-        {
-            tempAxis = r1 ^ r2;
-        }
-    }
-    else
-    {
-        tempAxis = r3 ^ r1;
-    }
-
-    radius_ = mag(r3);
-
-    // set up and return the local coordinate system
-    return cylindricalCS("arcEdgeCS", centre, tempAxis, r1);
+    centre_ = pM - l*axis/2 - rM*magChord/2/tan(degToRad(theta)/2);
+    axis_ = axis;
+    theta_ = degToRad(theta);
+    length_ = l;
 }
 
 
 // * * * * * * * * * * * * * * * * Constructors  * * * * * * * * * * * * * * //
 
-Foam::blockEdges::arcEdge::arcEdge
-(
-    const pointField& points,
-    const label start,
-    const label end,
-    const point& pMid
-)
-:
-    blockEdge(points, start, end),
-    p1_(points_[start_]),
-    p2_(pMid),
-    p3_(points_[end_]),
-    cs_(calcAngle())
-{}
-
-
 Foam::blockEdges::arcEdge::arcEdge
 (
     const dictionary& dict,
@@ -132,42 +111,54 @@ Foam::blockEdges::arcEdge::arcEdge
 )
 :
     blockEdge(dict, index, points, is),
-    p1_(points_[start_]),
-    p2_(is),
-    p3_(points_[end_]),
-    cs_(calcAngle())
-{}
+    p0_(points_[start_]),
+    p1_(points_[end_]),
+    centre_(),
+    axis_(),
+    theta_(),
+    length_()
+{
+    token firstToken(is);
+    is.putBack(firstToken);
+
+    if (firstToken == token::BEGIN_LIST)
+    {
+        const point pA(is);
+        calc(pA);
+    }
+    else
+    {
+        const scalar theta = readScalar(is);
+        const vector axis(is);
+        calc(theta, normalised(axis));
+    }
+}
 
 
 // * * * * * * * * * * * * * * * Member Functions  * * * * * * * * * * * * * //
 
 Foam::point Foam::blockEdges::arcEdge::position(const scalar lambda) const
 {
-    if (lambda < -small || lambda > 1 + small)
+    if (lambda < - small || lambda > 1 + small)
     {
         FatalErrorInFunction
             << "Parameter out of range, lambda = " << lambda
             << abort(FatalError);
     }
 
-    if (lambda < small)
-    {
-        return p1_;
-    }
-    else if (lambda > 1 - small)
-    {
-        return p3_;
-    }
-    else
-    {
-        return cs_.globalPosition(vector(radius_, lambda*angle_, 0.0));
-    }
+    const scalar t = theta_*lambda;
+    const vector r1 = p0_ - centre_, r2 = axis_ ^ r1;
+
+    return centre_ + r1*cos(t) + r2*sin(t) + axis_*length_*lambda;
 }
 
 
 Foam::scalar Foam::blockEdges::arcEdge::length() const
 {
-    return degToRad(angle_*radius_);
+    const vector r1 = p0_ - centre_;
+
+    // Length of a helical segment
+    return degToRad(theta_*sqrt(magSqr(r1) + sqr(length_)));
 }
 
 
diff --git a/src/mesh/blockMesh/blockEdges/arcEdge/arcEdge.H b/src/mesh/blockMesh/blockEdges/arcEdge/arcEdge.H
index 9cfdaed3fc..a9886bb573 100644
--- a/src/mesh/blockMesh/blockEdges/arcEdge/arcEdge.H
+++ b/src/mesh/blockMesh/blockEdges/arcEdge/arcEdge.H
@@ -25,7 +25,14 @@ Class
     Foam::blockEdges::arcEdge
 
 Description
-    Defines the arcEdge of a circle in terms of 3 points on its circumference
+    An arcEdge between two points on a circle. The arc is defined either by a
+    third point that the arc passes through, or by the angle of the sector and
+    the axis of the circle.
+
+    If the angle-axis specification is used, the axis may not be not
+    perpendicular to the line connecting the end points. In that case, the axis
+    is considered to be that of a cylinder, and the arc represents a portion of
+    a helix on the surface of that cylinder.
 
 SourceFiles
     arcEdge.C
@@ -36,7 +43,6 @@ SourceFiles
 #define blockEdges_arcEdge_H
 
 #include "blockEdge.H"
-#include "cylindricalCS.H"
 
 // * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
 
@@ -55,15 +61,34 @@ class arcEdge
 {
     // Private Data
 
-        point p1_, p2_, p3_;
-        cylindricalCS cs_;
-        scalar angle_;
-        scalar radius_;
+        //- The start point of the arc
+        const point p0_;
+
+        //- The end point of the arc
+        const point p1_;
+
+        //- The centre of the circle of which the arc is a part
+        point centre_;
+
+        //- The axis of the circle of which the arc is a part
+        vector axis_;
+
+        //- The sector angle of the arc
+        scalar theta_;
+
+        //- The axial length of the arc/helix
+        scalar length_;
+
 
     // Private Member Functions
 
-        //- Calculate the coordinate system, angle and radius
-        cylindricalCS calcAngle();
+        //- Calculate the coordinate system, angle and radius from a mid point
+        //  somewhere within the arc
+        void calc(const point& pM);
+
+        //- Calculate the coordinate system, angle and radius from a sector
+        //  angle and a normal to the plane of the arc
+        void calc(const scalar theta, const vector& axis);
 
 
 public:
@@ -74,14 +99,6 @@ public:
 
     // Constructors
 
-        //- Construct from components
-        arcEdge
-        (
-            const pointField& points,
-            const label start, const label end,
-            const point& pMid
-        );
-
         //- Construct from Istream setting pointsList
         arcEdge
         (
diff --git a/tutorials/basic/potentialFoam/cylinder/system/blockMeshDict b/tutorials/basic/potentialFoam/cylinder/system/blockMeshDict
index 8aace2d3c7..7766ff8e15 100644
--- a/tutorials/basic/potentialFoam/cylinder/system/blockMeshDict
+++ b/tutorials/basic/potentialFoam/cylinder/system/blockMeshDict
@@ -76,22 +76,22 @@ blocks
 
 edges
 (
-    arc 0 5 (0.469846 0.17101 -0.5)
-    arc 5 10 (0.17101 0.469846 -0.5)
-    arc 1 4 (0.939693 0.34202 -0.5)
-    arc 4 9 (0.34202 0.939693 -0.5)
-    arc 19 24 (0.469846 0.17101 0.5)
-    arc 24 29 (0.17101 0.469846 0.5)
-    arc 20 23 (0.939693 0.34202 0.5)
-    arc 23 28 (0.34202 0.939693 0.5)
-    arc 11 16 (-0.469846 0.17101 -0.5)
-    arc 16 10 (-0.17101 0.469846 -0.5)
-    arc 12 15 (-0.939693 0.34202 -0.5)
-    arc 15 9 (-0.34202 0.939693 -0.5)
-    arc 30 35 (-0.469846 0.17101 0.5)
-    arc 35 29 (-0.17101 0.469846 0.5)
-    arc 31 34 (-0.939693 0.34202 0.5)
-    arc 34 28 (-0.34202 0.939693 0.5)
+    arc 0 5 45.0 (0 0 1)
+    arc 5 10 45.0 (0 0 1)
+    arc 1 4 45.0 (0 0 1)
+    arc 4 9 45.0 (0 0 1)
+    arc 19 24 45.0 (0 0 1)
+    arc 24 29 45.0 (0 0 1)
+    arc 20 23 45.0 (0 0 1)
+    arc 23 28 45.0 (0 0 1)
+    arc 11 16 45.0 (0 0 -1)
+    arc 16 10 45.0 (0 0 -1)
+    arc 12 15 45.0 (0 0 -1)
+    arc 15 9 45.0 (0 0 -1)
+    arc 30 35 45.0 (0 0 -1)
+    arc 35 29 45.0 (0 0 -1)
+    arc 31 34 45.0 (0 0 -1)
+    arc 34 28 45.0 (0 0 -1)
 );
 
 boundary