By Jingshan Zhao
Advanced concept of Constraint and movement research for robotic Mechanisms presents an entire analytical method of the discovery of recent robotic mechanisms and the research of current designs in response to a unified mathematical description of the kinematic and geometric constraints of mechanisms.
Beginning with a excessive point advent to mechanisms and elements, the booklet strikes directly to current a brand new analytical thought of terminal constraints to be used within the improvement of latest spatial mechanisms and constructions. It essentially describes the appliance of screw concept to kinematic difficulties and gives instruments that scholars, engineers and researchers can use for research of severe components corresponding to workspace, dexterity and singularity.
- Combines constraint and loose movement research and layout, supplying a brand new method of robotic mechanism innovation and improvement
- Clearly describes using screw idea in robotic kinematic research, making an allowance for concise illustration of movement and static forces when put next to standard research methods
- Includes labored examples to translate thought into perform and reveal the appliance of recent analytical ways to serious robotics problems
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Additional resources for Advanced Theory of Constraint and Motion Analysis for Robot Mechanisms
Neither the magnitude of force f nor the angular velocity ω appears in this condition. Therefore, the condition where a rigid body keeps balance is only determined by the unit force screw and the unit motion screw. 94) $f = s2 . 96) where M12 is a scalar and it is called the reciprocal product of screws $ω and $ f . Two screws, whose reciprocal product is zero, are called a pair of reciprocal screws. 97) 48 Advanced Theory of Constraint and Motion Analysis for Robot Mechanisms where $1 = $ω ,$2 = $ f , = 0 I , 0 and I are 3 × zero matrix and unit I 0 matrix, individually.
1) can be expressed as S= L M N T . 8) where · denotes the norm of a three-dimensional vector “·”. 9) s= = ⎣m ⎦ S n where ⎧ ⎪ l = √ 2 L2 2 ⎪ ⎨ L +M +N m = √ 2 M2 2 L +M +N ⎪ ⎪ ⎩n = √ N . 10) Chapter | 2 A Brief Introduction to Screw Theory 31 Obviously, s = l 2 + m 2 + n 2 = 1. 11) Suppose that s0 = S0 . 12) where r × s = s0 . 11) are called unit screws. 12) is called the unit screw of a line, where s0 indicates the distance from the origin of coordinate system to the line. It is noteworthy that S0 is generally expressed as a function of S S0 = g S According to the definition of screws, we have g(S) = r×S + hS where r represents the position vector of any point on a screw axis and h is the pitch of the screw.
Therefore, ω will be a unit vector without special instructions in this book. As a result, it is available to establish the spatial motion equations for a rigid body. In order to verify the methodology, an example is presented below. 1. Universal couplings can be used to deliver rotation between two spatial intersecting axes. 3 shows the structure of a single universal coupling. The driving shaft 1 and driven shaft 3 both have planar forks on their ends. These two forks and the crosshead 2 are composed of two perpendicular revolute pairs B and C.
Advanced Theory of Constraint and Motion Analysis for Robot Mechanisms by Jingshan Zhao