By Xianwen Kong
This specific monograph makes a speciality of the systematic style synthesis of parallel mechanisms (PMs), a key factor within the artistic layout of a large choice of leading edge units corresponding to parallel manipulators, movement simulators, and haptic units. crucial studying for researchers, builders, engineers and graduate scholars with pursuits in robotics, this booklet covers the class of PMs in addition to supplying a lot of PMs able to be utilized in useful purposes.
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Extra info for Type Synthesis of Parallel Mechanisms (Springer Tracts in Advanced Robotics)
Sample text
Single-loop KC with an inactive joint of the PKC (also called the connectivity of the moving platform). C can be calculated using C = 6 − c. 19) where Ri is called the redundant DOF of leg i. 20) i=1 where R is called the redundant DOF of the PKC. Then, we obtain the mobility (or DOF) F of the PKC as m F =C+R =6−c+ Ri . 21) is usually instantaneous. When c, ci and Ri are the same in different general configurations, the DOF is full-cycle. 22) i=1 where ∆ is called the number of overconstraints (also passive constraints or redundant constraints) if ∆ > 0.
The characteristic of a compositional unit of this class is that all the axes of the R joints are always coaxial. The wrench system of this compositional unit is always a 2-ζ ∞ -3-ζ 0 -system [Fig. 16f], which includes all the ζ 0 whose axes intersect the axes of the R joints, all the ζ ∞ whose axes are perpendicular to the axes of the R joints and all the linear combinations of the above wrenches. A coaxial compositional unit is denoted by ()L . • Class 7 (Codirectional compositional units). Serial KCs composed of one or more P joints whose directions are parallel.
Throughout this book, ξ and ζ are respectively represented by arrows in solid line and arrows in dashed line. For convenience, ξ 0 , ξ ∞ , ζ 0 and ζ ∞ are used to represent a twist of 0-pitch, a twist of ∞-pitch, a wrench of 0-pitch and a wrench of ∞-pitch respectively. Based on the reciprocity condition of screws, we obtain the geometric relation between a twist system and its wrench system as follows: (a1) The axis of a ξ 0 is coplanar with the axis of any ζ 0 . (a2) The direction of a ξ∞ is perpendicular to the axis of any ζ 0 .