FORWARD KINEMATICS: THE DENAVIT-HARTENBERG ...

More documents

Recommendations

Info

92CHAPTER 3. FORWARD KINEMATICS: THE DENAVIT-HARTENBERG CONVENTION θ1 z0 y0 x0 θ2 z1 y1 x1 y2 y3 y4 z2 z3, z4 Figure 3.11: DH coordinate frame assignment for the SCARA manipulator. Table 3.5: Joint parameters for SCARA. Link ai αi di θi 1 a1 0 0 ⋆ 2 a2 180 0 ⋆ 3 0 0 ⋆ 0 4 0 0 d4 ⋆ ∗ joint variable step is to locate and label the joint axes as shown. Since all joint axes are parallel we have some freedom in the placement of the origins. The origins are placed as shown for convenience. We establish the x0 axis in the plane of the page as shown. This is completely arbitrary and only affects the zero configuration of the manipulator, that is, the position of the manipulator when θ1 = 0. The joint parameters are given in Table 3.5, and the A-matrices are as x2 x3 x4 θ4 d3
3.3. EXAMPLES 93 follows. A1 = ⎡ c1 ⎢ s1 ⎢ ⎣ 0 −s1 c1 0 ⎤ 0 a1c1 0 ⎥ a1s1 ⎥ 1 0 ⎦ (3.45) A2 = 0 ⎡ c2 ⎢ s2 ⎢ ⎣ 0 0 s2 −c2 0 0 0 0 −1 1 ⎤ a2c2 ⎥ a2s2 ⎥ 0 ⎦ (3.46) A3 = 0 0 0 ⎡ ⎤ 1 0 0 0 ⎢ 0 1 0 0 ⎥ ⎢ ⎥ ⎣ 0 0 1 d3 ⎦ 1 (3.47) A4 = 0 0 0 ⎡ c4 −s4 ⎢ s4 c4 ⎢ ⎣ 0 0 1 ⎤ 0 0 0 0 ⎥ ⎥. 1 d4 ⎦ (3.48) 0 0 0 1 The forward kinematic equations are therefore given by T 0 4 = A1 · · ·A4 = ⋄ ⎡ c12c4 + s12s4 ⎢ s12c4 − c12s4 ⎢ ⎣ 0 −c12s4 + s12c4 −s12s4 − c12c4 0 0 0 −1 ⎤ a1c1 + a2c12 a1s1 + ⎥ a2s12 ⎥ −d3 − d4 ⎦ 0 0 0 1 . (3.49)
Page 1 and 2: Chapter 3 FORWARD KINEMATICS: THE D
Page 3 and 4: 3.1. KINEMATIC CHAINS 73 z1 x0 y1 z
Page 5 and 6: 3.2. DENAVIT HARTENBERG REPRESENTAT
Page 13 and 14: 3.3. EXAMPLES 83 Step 9: Form T 0 n
Page 15 and 16: 3.3. EXAMPLES 85 x2 d2 x1 x0 d3 O2
Page 17 and 18: 3.3. EXAMPLES 87 Table 3.3: DH para
Page 19 and 20: 3.3. EXAMPLES 89 where r11 = c1c4c5
Page 21: 3.3. EXAMPLES 91 T 0 6 is then give
Page 25 and 26: 3.4. PROBLEMS 95 Figure 3.14: Two-l
Page 27 and 28: 3.4. PROBLEMS 97 Figure 3.18: Elbow
Page 29 and 30: 3.4. PROBLEMS 99 Figure 3.21: Rhino
Page 31 and 32: 3.4. PROBLEMS 101 Figure 3.23: GMF

FORWARD KINEMATICS: THE DENAVIT-HARTENBERG ...

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?