# ICubWaistLeftLegKinematics

This page describes how to construct the matrix T_RoLf whose definition is given in ICubForwardKinematics. The matrix is constructed in two steps i.e. T_RoLf = T_Ro0 * T_0n. The first matrix T_Ro0 describes the rigid roto-translation from the root reference frame to points in the
0*th* reference frame as defined by the Denavit-Hartenberg convention.
In this case T_Ro0 is just a rigid rotation which aligns the z-axis with the first joint of the waist.
The second matrix T_0n corresponds to the Denavit-Hartenberg description of the forward kinematic, i.e. the roto-translation from the 0th reference frame to the n*th* reference frame being n the number of degrees of freedom.

The matrix T_0n is itself the composition of n matrices as defined by the DH convention: T_0n = T_01 T_12 ... T_(n-1)n. Here is the updated matlab code for computing the forward kinematics with the Denavit Hartenberg notation Media: ICubFwdKinNew.zip.

The foot reference frame is located in the palm as shown in the CAD figure. The **x** axis is in **red**. The **y** axis is in **green**. The **z** axis is in **blue**.

Here is the matrix T_Ro0:

1 | 0 | 0 | 0 |

0 | 0 | 1 | -68.1 |

0 | -1 | 0 | -119.9 |

0 | 0 | 0 | 1 |

Here is the table of the actual DH parameters which describe T_01, T_12, ... T_(n-1)n.

Link i / H – D | Ai (mm) | d_i (mm) | alpha_i (rad) | theta_i (deg) |
---|---|---|---|---|

i = 0 | 0 | 0 | -pi/2 | 90 + (-44 -> +132) |

i = 1 | 0 | 0 | -pi/2 | 90 + (-119 - > +17) |

i = 2 | 0 | -223.6 | pi/2 | -90 + (-79 -> +79) |

i = 3 | -213 | 0 | pi | 90 + (-125 -> +0) |

i = 4 | 0 | 0 | -pi/2 | -42 -> +21 |

i = 5 | -41 | 0 | 0 | -24 -> +24 |