Advanced Theory of Constraint and Motion Analysis for Robot by Jingshan Zhao

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 present 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 parts, the publication strikes directly to current a brand new analytical conception of terminal constraints to be used within the improvement of recent spatial mechanisms and constructions. It in actual fact describes the appliance of screw conception to kinematic difficulties and offers instruments that scholars, engineers and researchers can use for research of severe components similar 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, taking into consideration concise illustration of movement and static forces compared to traditional research methods
  • Includes labored examples to translate idea into perform and show the appliance of recent analytical ways to serious robotics problems

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3! 44) yields exp ωt = I + + ω ω ω2 ω 2 t + 1 ω 5! 5 5 t + 1 ω 4! 4 4 ω t− 1 ω 3! 3 3 1− 1− 1 ω 2! 2 2 t + ··· t + ··· . 45) with trigonometric series yields exp ωt = I + ω sin ω ω t + ω2 ω 2 1 − cos ω t . 46) is called the Rodrigues formula [6]. 47) where θ denotes the angle with which the vector p rotates around the axis ω. 46) can be expressed as exp ωt = I + ω ω2 1 − cosθ . 3 37 Single universal coupling. 48) can be further simplified as exp ωt = I + ωsinθ + ω2 1 − cosθ . 49) when the direction of rotational axis, ω, and the rotated angle of θ are known.

Supposing that the length of the common perpendicular of the axes of $1 and $2 is denoted by d, and the intersections of the z-axis and the axes of $1 and $2 are o1 and o2 . 6 T . Reciprocal product of two screws. 97), the reciprocal product of screws $1 and $2 is M12 = $1T $2 = s1 · de3 × s2 + h 2 s2 + h 1 s1 · s2 = h 1 + h 2 s1 · s2 + ds1 · e3 × s2 . 6, the following equations hold s1 · s2 = cosα s1 · e3 × s2 = −sinα. 104) yields M12 = $1T $2 = h 1 + h 2 cosα − dsinα. 106) M12 is called the reciprocal distance between $1 and $2 .

M. J. Richard, Determination of maximal singularity-free zones in the six-dimensional workspace of the general Gough–Stewart platform, Mechanism and Machine Theory 42 (4) (2007) 497–511. Z. Yang, K. Q. Zhang, On the workspace boundary determination of serial manipulators with non-unilateral constraints, Robotics and Computer Integrated Manufacturing 24 (1) (2007) 60–76. -S. -L. -J. Feng, Symmetrical characteristics of the workspace shape for spatial parallel mechanisms with symmetric structure, Mechanism and Machine Theory 43 (4) (2008) 427–444.

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