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M1_1(A)

# M1_1(A) - NANYANG TECHNOLOGICAL UNIVERSITY G171 Laboratory...

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NANYANG TECHNOLOGICAL UNIVERSITY G171: Laboratory Experiment 1A Formal Report for Experiment M1 Study of Relative motion Lab Tutor: Jonathan Tai Chin Hoe Submitted by: Ong Hock Guan Lab Group: BL18

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CONTENTS Part 1: Four-bar linkage 1. Introduction page 3 2. Theory page 3-5 3) Objectives page 5 4) Experimental procedures page 6 5) Results & Discussion page 7-10 6) Further Discussion page 10-13 Part 2: Modeling of mechanisms 1) Introduction page 14 2) Objectives page 14 3) Software page 14 4) Procedure page 14 5) Calculations page 14-17 Conclusion page 18 References page 19 Appendix page 20 2
PART 1: FOUR-BAR LINKAGE Introduction All motions are relative. A basis fixed reference system refers to the reference system attached to the earth’s surface and absolute motion refers to any motion based on this fixed system. Relative motion is used to relate any motion that is observed relative to a well-defined moving reference system other than the basis fixed one. The term mechanism is applied to the combination of geometrical bodies, which constitute a machine or part of a machine. A mechanism may therefore be defined as a combination of rigid or resistant bodies, formed and connected so that they move with definite relative motions with respect to one another. The degrees of freedom are important when considering a constrained rigid body system that is a mechanism. It is less crucial when the system is a structure or when it does not have definite motion. Theory Relative motion: * A and B are moving particles, of positions vectors r A and r B . The position vector of A relative to B is: r A/B = r A r B ( Look at the figure ). => v A/B = d( r A - r B )/dt = d r A /dt - d r B /dt = v A - v B . => a A/B = d( v A/B )/dt = d( v A - v B )/dt = a A - a B . By the same way we can define the motion of B relative to A . Translational motion A point-attached translating reference system is one that moves in translation together with a point as the origin. 3

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In translational motion, we were able to characterize objects as point particles moving in a straight line. With rotational motion, much more than in translational motion, we consider objects not as particles, but as rigid bodies. Rotational motion A body-attached moving reference system is one that is fixed to a solid body and a point on the body is taken as the origin. The pose of a rigid body is defined by its position and attitude. POSITION: origin of local coordinate system with respect to global coordinates ATTITUDE: orientation of local coordinate system with respect to global axes A coordinate transformation can describe: (1) the relationship between coordinates in a global or local reference frame, and (2) the position and attitude of a moving body at each instant where: G: global coordinate system L: local coordinate system R G : vector from global origin to point P on the local body (equivalent to the global coordinates of P) R O : vector from the global origin to the local origin R L : vector from the local origin to point P (equivalent to the local coordinates of P) 4
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