For a 3-DOF robot, given the following transformations, find the Jacobian °J. G-Si 0 0 C2 -S2 0 0...
Question 3 a) For the 3-DoF robot in Figure 3, draw the frames if the D-H convention is used b) Using the D-H frames, express rotation matrix R as a function of 8,8... c) Solve the inverse kinematics problem, that is, 0.0... given a desired orientation defined by the rotation matrix: - Jq4. where d) Express the Jacobian matrix for the relationship velocity of frame 3 expressed within frame o. is the absolute angular Figure 3: 3-Dof robot with the...
SECTION B QUESTION 1 a) Given the arm matrix and the kinematics parameters of Spherical ARM robot as in Table Q1, calculate the manipulator Jacobian matrix. 10 0 51 1 ,002 01r- 105101 -S2 0 C2 0 1 0 S1 0 01 -10 1 0 01,12 L0 0 01 Table Q1 From Link Var 01 82-90 90 52C2 1-2 2 2-n 3 0° SECTION B QUESTION 1 a) Given the arm matrix and the kinematics parameters of Spherical ARM robot...
MATLAB EXERCISE 5 This exercise focuses on the Jacobian matrix and determinant, simulated resolved-rate control, and inverse statics for the planar 3-DOF, 3R robot. (See Figures 3.6 and 3.7; the DH parameters are given in Figure 3.8.) The resolved-rate control method [9] is based on the manipulator velocity equation x = kve, where ky is the Jacobian matrix, is the vector of relative joint rates, X is the vector of commanded Cartesian velocities (both translational and rotational), and k is...
2. Consider the 3-DOF robot configuration in the following figure. Using inverse kinematics, solve for (30 marks) 01.02 and 83, if the position and orientation of point P is given by: 0-1 P=10 Y2 Yor Y 2. Consider the 3-DOF robot configuration in the following figure. Using inverse kinematics, solve for (30 marks) 01.02 and 83, if the position and orientation of point P is given by: 0-1 P=10 Y2 Yor Y
IV. Consider the following game tree and the given choice functions for players P, Pa, and Ps. Draw the choice subtrees determined by P and c (label this as S1), Pa and c (label this as Sa), and Ps and cs (label this as Sa). Then determine the payoffs ,(S1, S2, Sa) for eachje {1,2,3) . (15 POINTS) ci(root) b, ca(a) = e, c2(b)= d; oa(d) h, cs(c) j P root b Pa a g P2 P3 ok (0,-1,1) e...
Question (2): (5 Marks) x-1-3-y x-1-6-y:+2 are (A) Determine intersecting or skew. If they intersect, find the point of intersection Given SI: x2-2y2 = 4z2-252 &s2: (0 Show that the tangent planes to the two surfaces at P(2,0,-8) are perpendicular. whether the lines parallel, 2-z & 12 Marks] 4x2 +9y2-24. (B) Find the points on Si at which the tangent plane is parallel to the plane x+y+32-5 3 Marks] Question (2): (5 Marks) x-1-3-y x-1-6-y:+2 are (A) Determine intersecting or...
3. You are given the following exchange rates: Exchange Rates Time 0 Time 1 So Si USD / GBP 1.8558 1.8561 USD/EUR 1.2674 1.2622 CAD / USD 1.3111 1.3129 MXN / USD 10.7575 10.6780 AUD/USD 1.3095 1.3025 ZAR / USD 6.8330 6.8850 Where: GBP = British Pound: CAD Canadian Dollar; MXN - Mexican Peso; AUD = Australian Dollar; ZAR = South African Rand Using the information above: a. Which foreign currencies are directly quoted? b. Which foreign currencies are indirectly...
Q4 only: Question 3. Consider the region of R3 given by V is bounded by three surfaces. Si is a disc of radius 1 in the plane z -0. S3 is a disc of radius 2 in the plane z 3 and a) Make a clear sketch of V. (Hint: You could consider the cross-section of S2 with y-0, and then use the circular symmetry. (b) Express V in cylindrical coordinates. (c) Calculate the volume of V, working in cylindrical...
Given that lim f(x) = 3, lim g(x) = 0, and lim h(x) = 5, find the limits that exist. Enter DNE if the limit doesn't exist help (limits) (a) lim f(x) + h(x)] = 8 (b) lim{f(x)} = 9 (c) lim yh(x) = 5^(1/3) help (limits) !!! help (limits) help (limits) In help (limits) help (limits) f(3) (2) (9) lim !!! help (limits) 3-a g(x) 2f(x) !! help (limits) h(x) - f(x)
The state space model of an interconnected three tank water storage system is given by the following equation: -3 1 0 1rh dt os lo 0 3] 10 1-3 The heights of water in the tanks are, respectively, h,h2,h3. Each tank has an independent input flow; the volume flow rates of input water into the three tanks are, respectively, qǐ1,W2,4a. Each tank also has a water discharge outlet and the volume flow rates of water coming out of the tanks...