Multi-Arm Cooperating Robots- Dynamics and Control - Zivanovic and Vukobratovic Part 2 docx

... q 1 2 + l 2 2 cos(q 1 2 + q 2 2 ) + l 3 2 cos(q 1 2 + q 2 2 + q 3 2 ) + l 4 2 cos(q 1 2 + q 2 2 + q 3 2 + q 4 2 ) z o2 + l 1 2 sin q 1 2 + l 2 2 sin(q 1 2 + q 2 2 ) + l 3 2 sin(q 1 2 + q 2 2 + ... l 1 2 cos q 1 2 + l 2 2 cos(q 1 2 + q 2 2 ) + l 3 2 cos(q 1 2 + q 2 2 + q 3 2 ) + l 4 2 cos(q 1 2 + q 2 2 + q 3 2 + q 4 2 ) z o2...

Ngày tải lên: 10/08/2014, 05:20

... = 1 2 F 12 y 12 + 1 2 F 23 y 23 = 1 2 c p y 2 12 + 1 2 c k y 2 23 = 1 2 c p (y 1 − y 2 ) 2 + 1 2 c k (y 2 − y 3 ) 2 = 1 2 c p (Y 1 − Y 2 + s 1 ) 2 + 1 2 c k (Y 2 − Y 3 + s 3 ) 2 = 1 2 π 12 (Y 1 − ... defined by π 12 = π 21 = c p  1 + s 1 ||Y 1 − Y 2 ||  2 = c p  1 − Y 10 − Y 20 ||Y 1 − Y 2 ||  2 , π 23 = π 23 = c k  1...

Ngày tải lên: 10/08/2014, 05:20

... is L = T −  = 1 2 m( ˙ Y 10 +˙y 2 ) 2 − 1 2 c p (y 1 − y 2 ) 2 − 1 2 c k (y 2 − y 3 ) 2 (38) = 1 2 m( ˙ Y 10 +˙y 2 ) 2 − 1 2 c p (Y 1 − Y 2 + s 1 ) 2 − 1 2 c k (Y 2 − Y 3 + s 3 ) 2 , so that the ... −c k c k ⎤ ⎦ · ⎡ ⎣ y 1 y 2 y 3 ⎤ ⎦ = 1 2 y T Ky, y = col(y 1 ,y 2 ,y 3 ), ( 32)  = 1 2 ⎡ ⎣ Y 1 Y 2 Y 3 ⎤ ⎦ T ⎡ ⎣ π 12 −π 12 0 −π 12 π 12 +...

Ngày tải lên: 10/08/2014, 05:20

... quantities (see relations (27 ), (28 ), (29 ) and (31)). A d = 1 2  T F int = 1 2  T π  , (68) where F int = F int (Y ) and  = (Y) are the vectors of internal forces and relative displacements ... diag(K e1 ,K e2 ,K e3 , ),andex- panded vectors of the force F e = column(F e1 ,F e2 ,F e3 , ) and displacement  e = column( e1 , e2 , e3 , ). If the equations of stiffness of...

Ngày tải lên: 10/08/2014, 05:20

... 0  r ia +ˆη − (r ja +ˆη)  2 I 3×3 ,c ψ ij ,c θ ij ,c ϕ ij  = diag  c ij  1 − ρ ij 0  r ia − r ja   2 I 3×3 ,c ψ ij ,c θ ij ,c ϕ ij  = π ij (Y i ,Y j ) ( 129 ) 92 Multi-Arm Cooperating Robots of ... R 6m+6 . (114) 88 Multi-Arm Cooperating Robots Y Ii =  r ia A ia  +  ˆη 0  = Y i + η i = Y i +¯η, i = 0, ,m. ( 123 ) The overall potential energy at that point is 2...

Ngày tải lên: 10/08/2014, 05:20

... Figure 22 d. Simulation results for τ 1 1 = 50 [Nm] and τ 1 2 =−50 [Nm] 1 32 Multi-Arm Cooperating Robots part referring to the physical quantity used in modeling and the number indicat- ing the ... 21 b. Simulation results for τ j i = 0, i, j = 1, 2, 3 128 Multi-Arm Cooperating Robots 133 Figure 22 e. Simulation results for τ 1 1 = 50 [Nm] and τ 1 2 =−50 [Nm] Mathem...

Ngày tải lên: 10/08/2014, 05:20

... R 6×1 , W s (Y s ) = diag(W 2 (Y 2 ), ,W m (Y m )) ∈ R (6m−6)×(6m−6) , F bs (Y s , ˙ Y s ) = col(F b2 (Y 2 , ˙ Y 2 ), ,F bm (Y m , ˙ Y m )) = col  ˙ W 2 (Y 2 ) ˙ Y 2 − ∂T 2 (Y 2 , ˙ Y 2 ) ∂Y 2 , , ˙ W m (Y m ) ˙ Y m − ∂T m (Y m , ˙ Y m ) ∂Y m  ∈ ... equations (21 7) and (21 8), differential equations should be solved. Using the indexing system defined in (20 6), (20 7...

Ngày tải lên: 10/08/2014, 05:20

... c k )Y 2 − c k Y 3 + mg and F c = (F c1 ,F c2 ) T . Models of the manipulators are taken in the form m 1 ¨q 1 + m 1 g = τ 1 + f c1 ,f c1 =−F c1 , m 2 ¨q 2 + m 2 g = τ 2 + f c2 ,f c2 =−F c2 . (26 2) Kinematic ... determined. Synthesis of Nominals Figure 28 . Nominal input to a closed-loop cooperative system for gripping 1 82 Multi-Arm Cooperating Robots 169 ping F s e0 is det...

Ngày tải lên: 10/08/2014, 05:20

... of time for the non-controlled object and of time and state for the controlled object. For the con- 20 0 Multi-Arm Cooperating Robots For a linear system of n x ordinary first-order differential ... torques τ ,andthe 20 4 Multi-Arm Cooperating Robots 20 3 – elastic; • in view of their redundanc y – non-redundant, and – redundant; • in view of joint compliance – with non-compli...

Ngày tải lên: 10/08/2014, 05:20