Motion Simulation
Developing the simulation of the robotic gripper’s motion involved implementing the determined equations into a Matlab code that plotted the coordinate of each joint. These coordinates were connected through line functions that would assemble to create the virtual representation of the proposed design. The full program can be found in Appendix C.
In this program, the domain of θ2 is first declared to range from 0o to 360o per the design constraints. For the purpose of communicating the motion on a plot, this range is split into twenty 18o increments as seen in Figures 3.2.1 to 3.2.3. The known parameters are then stated, starting from the link dimensions to the angles of θ5 as well as ⍺, the angle link h makes with Link 4, and ϕ, the angle between Link h and Link q. The equations for the length of theoretical Link 1 and the angles ꞵ2 and θ2p are also stated. Next, the ‘Equations’ portion of the program describes the simplifying equations derived from Appendix A followed by the equations of the angular displacements or dependent variables, θ3p and θ4p from the appointed four-bar loop. Using these variables, the coordinates of each joint in the five-bar mechanism and claw can be expressed. This is using point O2 as the origin, hence ‘xO2’ and ‘yO2’ are both set to zero in lines 50-51 (Appendix C). Equations that require the angle of θ3 or θ4 to describe its position are described by adding ꞵ2 to θ3p and θ4p such as the coordinates of points B, F and C in Figure 3.1.1(b). Finally, utilizing MATLAB’s line function, each link was plotted by connecting each joint or coordinate with a line. Link 1 and 5 are coded with blue, Link 2, 3, and 4 are coded with red, and the claw (Link h and q) is coded with magenta. The resulting simulations are as follows:
(a) Motion Without Claw (b) Motion with Claw
Figure 3.2.1. Matlab Five-Bar Motion Simulation (θ5=30o, 0o < θ2 < 360o)
(a) Motion without Claw (b) Motion with Claw
Figure 3.2.2. Matlab Five-Bar Motion Simulation (θ5=45o, 0o < θ2 < 360o)
(a) Motion without Claw (b) Motion with Claw
Figure 3.2.3. Matlab Five-Bar Motion Simulation (θ5=60o, 0o < θ2 < 360o)
From these results, the maximum and minimum achievable angle for θ4 could be obtained as well as the angle of θ2 at which they occur. For the purposes of design for a physical prototype, the range of θ2 that was used for consideration ranged from 0o to 180o. Doing this revealed the motion limitations of the five-bar mechanism or more specifically, Link 4, and provided the necessary information needed to design the claw so that the ranging diameter of 0cm to 10cm requirement could be met. This would then go on to establish the specific configuration in which the force analysis bases its calculations on.
From the range of motion, previously determined from the motion analysis, the initial lengths of the links for the mechanism were chosen arbitrarily. These lengths were then analyzed and the range of motion at which the mechanism fully closes and opens was determined. It was then determined that at the constraining angles for link 5 at 30, 45 and 60 degrees, the mechanism is fully open at 162 degrees and fully closed at 36 degrees. The lengths of the initial links can be seen in Table 3.2.1