# ICubWaistLeftLegKinematicsV2.5

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 0th 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 nth 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 at its sole 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 a_i (mm) d_i (mm) alpha_i (rad) theta_{i} + (ang. range) (deg)
i = 0 0 0 -pi/2 90 + (-44 -> +132)
i = 1 0 0 -pi/2 90 + (-119 - > +17)
i = 2 -0.9175 -234.545 pi/2 -90 + (-79 -> +79)
i = 3 -200.5 0 pi 90 + (-125 -> +0)
i = 4 0 0 -pi/2 0 + (-42 -> +21)
i = 5 -68.05 -3.5 0 0 + (-24 -> +24)