MEEG439_LEC1 - Mechanisms Modeling and Analysis Purpose: 1....

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Mechanisms Modeling and Analysis Purpose: 1. Provides insight and intuition about the deice 2. Low cost of a model compared to actual device 3. Safer, cheaper, faster 4. Better Final Results General Approach: The idea is to replace the physical elements of the mechanism with representative vector elements. Since vectors are mathematical descriptors of physical objects, they can be combined in equations and solved. Constraints will define connections between and motion of vectors. Thus, it will behave like the actual system during analysis. Note: Advanced models may include constraints such as friction, joint limits, interference, etc.
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Building analytical models: Start with individual component models 1. Binary links: Replace with a single vector from one revolute to the next. Length is assumed known (since it is constant) and angle is unknown if it is not an input. 2. Ternary links: Two vectors (of constant and assumed known) length will represent this link. The vectors are separated by a constant angle (since it is fixed, it is assumed to be known). Thus, there is only one unknown in this system.
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Building blocks (cont.) 3. Revolute joints: Revolute joints attach links allowing one degree of freedom motion, and show up in loop closure equations. 4. Slider elements: Represent sliders with a vector, running along the axis of the slider, starting from some reference. This vector has a variable length (unknown unless driven) and either fixed or variable angle.
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5. Sliders on curved beams: Referring to the fig. Below, C = center of curvature, R is from ground to C , and r is from C to P . Note that in an instantaneous sense, R is constant relative to the bar, and r has constant length. Thus, the only unknown in referencing
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MEEG439_LEC1 - Mechanisms Modeling and Analysis Purpose: 1....

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