Question

${^n}T_{n+1} = \begin{bmatrix} C\theta_{n+1} & -S\theta_{n+1}C\alpha_{n+1} & S\theta_{n+1}S\alpha_{n+1} & a_{n+1}C\theta_{n+1} \\ S\theta_{n+1} & C\theta_{n+1}C\alpha_{n+1} & -C\theta_{n+1}S\alpha_{n+1} & a_{n+1}S\theta_{n+1} \\ 0 & S\alpha_{n+1} & C\alpha_{n+1} & d_{n+1} \\ 0 & 0 & 0 & 1 \end{bmatrix}$

          ${^n}T_{n+1} = \begin{bmatrix} C\theta_{n+1} & -S\theta_{n+1}C\alpha_{n+1} & S\theta_{n+1}S\alpha_{n+1} & a_{n+1}C\theta_{n+1} \\ S\theta_{n+1} & C\theta_{n+1}C\alpha_{n+1} & -C\theta_{n+1}S\alpha_{n+1} & a_{n+1}S\theta_{n+1} \\ 0 & S\alpha_{n+1} & C\alpha_{n+1} & d_{n+1} \\ 0 & 0 & 0 & 1 \end{bmatrix}$

Added by Robert P.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Christopher Dzorkpata

Step 1

The z-axis is along the axis of rotation of the joint, the x-axis is along the direction of the link, and the y-axis is determined by the right-hand rule. - The origin of the second joint (Joint 2) is at the end of the first link. The z-axis is along the axis of Show more…

Show all steps

Thanks for your feedback!

For the SCARA robot manipulator given in the figure: a) Insert a coordinate system for each joint. b) Prepare the table showing the Denavit-Hartenberg parameters. c) Find the transformation matrix of each joint. d) Find the forward kinematics between the main frame (fixed axes) and the end function. 01 da CO+1-SOn+1Can+1 SOn+1Sa+1 a+1COn+1 SO+1 CO+1Can+1 -CO+1San+1an+1SO+1 T+1= 0 San+1 Can+1 I+up 0 0 0 1