Body kinematics

Forward kinematics (FK)

When listing out the sequence of transformations required to perform a certain walk of the kinematic chain, always do the translation first, followed by the rotation. So for example

$${\vec{p}}_2=F_2^0{\vec{p}}_2^2=F_1^0{F}_2^1{\vec{p}}_2^2=H_T({\vec{d}}_1^0)H_R(\overrightarrow{{\theta }_1})H_T({\vec{d}}_2^1)H_R(\overrightarrow{{\theta }_2})\left[\begin{array}{c}0\\ 0\\ 0\\ 1\end{array}\right]$$

Notice how $F_i^j$, a Homogeneous transformation matrix, gets decomposed into the translation portion, followed by rotation.