tailieunhanh - Method of transmission matrix for investigating planar relative motions

In the paper [2] the method of transmission matrix applying for the case of a loop with turning pairs investigated. In the present paper the kinematics of a loop connected by composite joints, . the one of revolute-translational joints are discussed now. By means of proposed method the planar motion of rigid bodies is presented by a point of general view. | Vietnam J ournal of Mechanics, VAST, Vol. 29, No. 2 (2007), pp. 105 - 116 METHOD OF TRANSMISSION MATRIX FOR INVESTIGATING PLANAR RELATIVE M OTIONS Do SANH Hanoi University of Technology Do DANG KHOA University of Texas at Austin, USA Abstract . In the paper [2] the method of transmission matrix applying for the case of a loop with turning pairs investigated . In the present paper the kinematics of a loop connected by composite joints, . the one of revolute-translational joints are discussed now . By means of proposed method the planar motion of rigid bodies is presented by a point of general view . Especially,the introduced method allows to apply effectively universal softwere, for example, MATCAD, MAPLE, . for investigating complex mechanical systems. 1. GENERA L INFORMATIONS AB OUT T R ANSMIS SION MAT R IX METH OD Let us consider a figure S rotating about 0 of the frame of reference Ox' y' and oriented by the y' angle in counteroclockwise direction. This frame oy y of reference is in translational displacement with respect to t he fixed frame of reference 0 0 °x 0 y . As is known, the last fr ame is refered to global or inerx tia frame of reference. An other frame of reference Oxy rigidly connected to the figure S at its point u 0 is assigned a body frame of reference. Let us consider a point of the figure S. Its coordinates in these frame of reference are named global - coordi:•V nate and body-coordinate respectively. It is noticed : that the body-coordinates are constants, while the oo;._ 0 x global-coordinates are changing quantities at time. Fig. 1 Let us interest a point M connected rigidly to the figure S . Its components of bodycoordinates are denoted by the constants a and b. It is easy to establish the relationship between the components of global-coordinates and body-coordinates. That are I (1. 1) where u, v are the components of global-coordinate of the origin 0 . The expression ( 1. 1) can be written in the matrix .