机械应用力学版.ppt

3.8 Kinematic Mechanisms By Xin Wang Instructed by Qing Zhang Faculty of Mechanical Engineering Applied Dynamics Contents Analysis of Motion in a Closed Kinematic Chain: Method 1: Geometric and trigonometric method. (Example 3.6 Slider Crank) Method 2: Vector calculus. (Example 3.7 4-Bar Closed Chain) Grübler’s Mobility Criterion: Topological Invariants in Linkages Centrodes: Mechanisms as Rolling Motions Application of Centrodes to Biomechanics Reuleaux’s Method for Constructing Centrodes Example 3.6 Slider Crank A C L r Fig.3.16a Slider crank mechanism (Page110) or differentiate B Example 3.7 4-Bar Closed Chain A B C D r1 L Fig3.16b 4-bar planar linkage Point C can be described as: Using the angular-velocity cross-product theorem, differentiate it, then: One can show that: Example 3.7 4-Bar Closed Chain The determinant of the previous 2*2 matrix is: If There will be no solution for This points are called singular point, and usually would be avoided Topological Invariants in Linkages The concept of degrees of freedom: Rigid body in the plane: 3 degrees of freedom ( 2 translations and 1 rotation) Rigid body in the space: 6 degrees of freedom ( 3 translations and 3 rotations) Mobility(F): the number of degrees of freedom. For F=1: we can get: (The number of revolute or cylindrical joints) Topological Invariants in Linkages The integer requirement implies that the number of links n must be even, which leads to the sequence of possible single degree of freedom compound mechanisms: Mobility for Spatial Mechanisms Assuming that each kinematic pair can be assigned an integer measure of freedom for the th joint. Thus each joint reduces the mobility by so that the combined mobility of the mechanism becomes: If there are g joints, then this relation becomes: Centrodes: Mechanisms as Rolling Motions Older text: All planar motions are equivalent to pure rolling. Euler: Any finite motion can be se