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The two slider-crank mechanisms in the panda model are analyzed individually as two separate fourbar non-offset inversion #1 slider-crank linkage mechanisms in the XY Plane (2-Dimensional). The two mechanisms are analyzed separately, since it makes it easier to perform the vector loop position, velocity, and acceleration approach analysis on mechanisms that each have one input, one output, and one degree-of-freedom. Thus, we will first perform position, velocity, and acceleration analysis on the fourbar horizontal non-offset inversion #1 slider-crank mechanism that is comprised of four-bar linkages and has one degree of freedom. Then, we will perform position, velocity, and acceleration analysis on the fourbar vertical non-offset inversion #1 slider-crank mechanism. Kinematic still drawings of both slider-crank mechanisms are illustrated below.
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Fig.2 Kinematic drawing of
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Horizontal slider-crank mechanism (for bamboo stick)
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Fig.1 Kinematic drawing of vertical slider-crank mechanism (for lower jaw)
3.1 Given/measured parameters for both slider-crank mechanisms
Fig. 3MATLAB given/measured parameters
The known parameters prior to performing kinematic analysis of each fourbar slider-crank mechanism are shown in Fig.13. Both fourbar slider-crank mechanisms have the same link length values and configuration (open). The constant link length values (input crank length (a), coupler rod length(b), and ground offset (c)), were obtained by measuring each link with a ruler in units of millimeters. Link c (offset ground length) is 0mm because the slider axis extended passes through the crank pivot. Thus, this means both slider-crank mechanisms are fourbar non-offset inversion #1 slider-crank mechanisms, where the slider block translates (Norton).
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Given all the measured parameters that we know, shown in fig. ### we 3 we are able to perform a position analysis on each slider-crank mechanism, in order to find its coupler bar angle (theta3) , and its ground slider position length from the crank pivot (d). To begin the analysis of each slider-crank mechanism, the linkages of the mechanism are represented as position vectors as shown in Fig. ### 4-5 below. The position vector R4 is 0, since the mechanism is a fourbar non-offset inversion #1 slider-crank. A closed vector loop equation (1) shown below represents the vector positions in the mechanism.
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fig. 4 Position Vector Loop Horizontal Slider-Crank Mechanism fig. 5 Position vector loop vertical slider-crank mechanism
R2 –R3 – 0 – R1 = 0 (1)
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3.3.2 Velocity Analysis Results for both Horizontal and Vertical Slider-Crank Mechanisms
The slider velocity vs input crank angle plot and slider velocity vs time plot both show that as the lower jaw and bamboo stick both hit their maximum displacements, their velocities are zero and while the jaw and bamboo stick are at distance halfway (24mm) between the maximum displacement and zero displacement, their velocities are at their maximum. The slider velocity vs time plot also illustrates that despite the vertical ground/slider link and input crank angle being offset by 90 degrees, both the vertical and horizontal mechanisms make a complete revolution in the same amount of time. Therefore, it is shown that both the panda’s lower jaw (vertically) and bamboo stick (horizontally) have the same velocities at the exact same time.
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