From f9f4f07a16e4afe55b9213c9c8160a3164017bb0 Mon Sep 17 00:00:00 2001
From: Peter Corke <peter.i.corke@gmail.com>
Date: Mon, 19 Oct 2026 18:13:48 +1000
Subject: [PATCH] docs(notebooks): modernise two-link-dynamics.ipynb, including
 the sign convention of gravity

Co-Authored-By: Claude Sonnet 5.5 <noreply@anthropic.com>
---
 docs/notebooks/two-link-dynamics.ipynb | 69 ++++++++++++++------------
 1 file changed, 38 insertions(+), 31 deletions(-)

diff --git a/docs/notebooks/two-link-dynamics.ipynb b/docs/notebooks/two-link-dynamics.ipynb
index a5b450c2e..00a15e496 100644
--- a/docs/notebooks/two-link-dynamics.ipynb
+++ b/docs/notebooks/two-link-dynamics.ipynb
@@ -4,8 +4,29 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "# Dynamics of 2-link manipulator\n",
+    "<!-- RTB_HEADER -- generated from the notebook metadata (rtb_header) by sync_bootstrap.py, do not hand-edit -->\n",
+    "<table>\n",
+    "  <tr>\n",
+    "    <td><div align=\"left\"><font size=\"30\">Robotics Toolbox for Python</font></div></td>\n",
+    "    <td><img src=\"figs/RobToolBox_RoundLogoB.png\" width=\"300\"></td>\n",
+    "  </tr>\n",
+    "</table>\n",
     "\n",
+    "<p></p>\n",
+    "<div align=\"center\" style=\"font-size: 1.5em;\">Dynamics of a 2-link manipulator</div>\n",
+    "<p></p>\n",
+    "\n",
+    "(c) Peter Corke 2026\n",
+    "\n",
+    "The gravity and velocity torques of the two-link planar arm in Spong, Hutchinson and Vidyasagar, computed by the Toolbox from a DH model and from an ETS model, and compared with the analytic Euler-Lagrange equations.\n",
+    "\n",
+    "> **Modernised 2026-10-19** to address API drift: this notebook was written for an earlier release of the Toolbox, and has been updated so that it runs with the current one."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
     "![Spong book](figs/spong-2link.png)\n",
     "\n",
     "Reference:\n",
@@ -75,7 +96,7 @@
    "metadata": {},
    "outputs": [],
    "source": [
-    "from roboticstoolbox import DHRobot, RevoluteDH, ERobot, ELink, ETS\n",
+    "from roboticstoolbox import DHRobot, RevoluteDH, Robot, Link, ET\n",
     "from math import pi, sin, cos\n",
     "import numpy as np\n",
     "\n",
@@ -119,14 +140,14 @@
    "source": [
     "L1 = RevoluteDH(a=l1, m=m1, r=[-lc1, 0, 0])\n",
     "L2 = RevoluteDH(a=l2, m=m2, r=[-lc2, 0, 0])\n",
-    "robot = DHRobot([L1, L2], gravity=[0, g, 0])"
+    "robot = DHRobot([L1, L2], gravity=[0, -g, 0])"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "The DH notation only allows rotation about the z-axis, which is out of the page in the Figure above.  Gravity acts downward so we set the gravity acceleration to be `[0, g, 0]` - accelerating upward at `g` provides the weight force experienced on Earth."
+    "The DH notation only allows rotation about the z-axis, which is out of the page in the Figure above.  The `gravity` argument is the acceleration due to gravity, a vector in the world frame.  Gravity acts downward, in the $-y$ direction of the figure, so we set it to `[0, -g, 0]` (the default is `[0, 0, -9.81]`).  The gravity load is the torque the joints must exert to hold the arm still against gravity, so it is positive for an arm stretched out horizontally."
    ]
   },
   {
@@ -136,7 +157,7 @@
    "outputs": [],
    "source": [
     "print(robot)\n",
-    "print(robot.dyntable())"
+    "print(robot.dynamics())"
    ]
   },
   {
@@ -268,7 +289,7 @@
     "\n",
     "L1 = RevoluteDH(a=l1, m=m1, r=[-lc1, 0, 0])\n",
     "L2 = RevoluteDH(a=l2, m=m2, r=[-lc2, 0, 0])\n",
-    "robot = DHRobot([L1, L2], gravity=[0, g, 0], symbolic=True)\n",
+    "robot = DHRobot([L1, L2], gravity=[0, -g, 0], symbolic=True)\n",
     "\n",
     "\n",
     "q = symbol(\"q_:2\")\n",
@@ -280,7 +301,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "## ERobot notation"
+    "## ETS notation"
    ]
   },
   {
@@ -324,9 +345,9 @@
    "metadata": {},
    "outputs": [],
    "source": [
-    "L1 = ELink(ets=ETS.rz(), m=1, r=[0.5, 0, 0], name=\"L1\")\n",
-    "L2 = ELink(ets=ETS.tx(1) * ETS.rz(), m=1, r=[0.5, 0, 0], parent=L1, name=\"L2\")\n",
-    "robot = ERobot([L1, L2], gravity=[0, g, 0])"
+    "L1 = Link(ets=ET.Rz(), m=1, r=[0.5, 0, 0], name=\"L1\")\n",
+    "L2 = Link(ets=ET.tx(1) * ET.Rz(), m=1, r=[0.5, 0, 0], parent=L1, name=\"L2\")\n",
+    "robot = Robot([L1, L2], gravity=[0, -g, 0])"
    ]
   },
   {
@@ -340,27 +361,6 @@
     "    tau_el = EL_grav(q)\n",
     "    print(tau_rne, \"vs\", tau_el)"
    ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": []
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": []
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": []
   }
  ],
  "metadata": {
@@ -409,6 +409,13 @@
     "_Feature"
    ],
    "window_display": false
+  },
+  "rtb_header": {
+   "title": "Dynamics of a 2-link manipulator",
+   "paragraphs": [
+    "The gravity and velocity torques of the two-link planar arm in Spong, Hutchinson and Vidyasagar, computed by the Toolbox from a DH model and from an ETS model, and compared with the analytic Euler-Lagrange equations."
+   ],
+   "modernised": "2026-10-19"
   }
  },
  "nbformat": 4,