A mobile platform with body frame named Fame1 is located initially in the positon [X0= 2000; y0=2000; z0=1000] of the global reference frame Frame0, and the orientation of Frame1 is intially identical to the Frame0. Then the platform starts to move along a trajectory that is defined by the profile [x0+200*t; y0+100*t; z0+300*sin(pi/2*t)] w.r.t global Frame in time t, and at the same time the Frame1 is also rotating aroud its own Z axis with constant velocity pi/2/second in rad. An industrial robot is installed on the platform and the robot reference frame coincides with the Frame1. At the time zero, the robot end-effector with a reference frame named Frame2 is locted at [500; 300; 400] w.r.t robot reference frame. After 45 seconds, the end-effector has travelled a distance of [500*sin(pi/4*t); 500*sin(pi/4*t); 500*sin(pi/2*t)] w.r.t its own robot reference frame, and at the same time the end-effector rotates around its x axis 60 degrees. . Compute the location and roll-pitch-yaw of the robot end-effector after 45 seconds with respect to (w.r.t) global frame. % write you codes here to compute t_1 = 45; % unit: second % inital location Ро = [2000; 2000; 1000]; % unit: mm

The vector expressions for the position vectors for cables “AC” and “AD” are given by: rAC = -3i - j - 6k ft and rAD = ­ 2i + 3j - 6k ft respectively.  What is the length of cable “AD”?

secondary spacecraft reference plane primary spacecraft primary orbit plane Once you fix the primary or target spacecraft (the selection of primary spacecraft is only a matter of context), the relative motion of the secondary spacecraft is governed by the following initial value problem: a" 2wy - 3w? a = fz; x (0) = *0, x' (0) = x, y" + 2wa' = fy; y (0) = Yo, Y (0) = % 2' + w? z = fa; z (0) = 20; z' (0) Where w stands for the mean angular velocity of the primary spacecraft within its orbit plane. Also, fy represents the differential acceleration on the secondary spacecraft. fz x (t) Assuming there is no external force acting on the secondary spacecraft, use Laplace Transform to determine its position y (t) in the space. Your z (t) answer will be in terms of w and the set of intial conditions. Hint: The z part of the given IVP is a second order IVP by itself. Therefore it can be solved for z using Laplace Transform. For each of the first two differential equations (from the top), begin…

cos (8, + 02). The orientation of an object in 3D is given as: [cos (8, + 02) 0 - sin (0, + 02)1 R = Lsin (0, + 02) 0 cos (0, + 02) Where 0, and 0, are functions of time. Find the angular velocity matrix and the angular velocity vector of the object.