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4.7 Chebyshev's Mechanism Analysis

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4.7 Chebyshev's Mechanism Analysis
4.2.6 Robert’s Mechanism

Fig. 4.13: The Robert’s Mechanism

Robert‘s linkage is another four-bar approximate straight line generator mechanism with coupler point C. Good results can be obtained with construction parameters d = 1, b
= 0.538 , a = c = 0.530 e = f = 1.04. Robert‘s mechanism generates a curve which has a

linear part parallel to the base link. Links and coupler curve are symmetric.[20]

The limitation of this mechanism is that the straight line path is very short. So whole wall cannot be covered while painting it. Therefore it cannot be used.

4.2.7 Chebyshev’s Mechanism

Fig. 4.14: The Chebyshev’s Mechanism
Link CB with E as its midpoint traces a straight horizontal line for most
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4.17: Lead Screw Design and Selection

One of the common issues in using lead screws – especially for the positioning applications – is backlash. Backlash means free axial movement between screw and nut or it can be said as the axial distance due to which the nut can be moved without turning the lead screw. Among the problems caused by backlash are the deterioration of the positioning accuracy and diminished repeatability of the performed task by the lead screw drive.[23] Fig. 4.18: Meshing “stub Acme” lead screw and nut (cut view). Detail: radial and axial clearances

Various anti-backlash nuts are designed and offered to address these problems. These nuts generally are made of two halves connected with preloaded springs that can move with respect to one another to compensate backlash and wear. The drawback of using these nuts is in the increased friction force, which lowers the efficiency and increases the required driving torque.
This lead screw mechanism can be used for wall painting purpose. For this, the screw will be held vertical with help of some support. Then over the nut a mechanism will be placed which will be comprising of a paint brush. Now when the nut will move up and down, the paint brush will also move with it and paint stroke will occur on
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The individual joint motions associated with these two categories are sometimes referred to by the term ―degrees of freedom‖, and a typical industrial robot is equipped with 4 to 6 degrees of freedom.[24]
The robot motions are accomplished by means of powered joints. Connecting the various manipulator joints together are rigid members that are called links. The joints used in the design of industrial robots typically involve a relative motion of the adjoining links that is either linear or rotational. Linear joints involve a sliding or translational motion of the connecting links. This motion can be achieved in a number of ways (e.g., by a piston, a telescoping mechanism, and relative motion along a linear track or rail).
There are at least three types of rotating joint that can be distinguished in robot manipulators.
The arm and body joints are designed to enable the robot to move its end effector to a desired position within the limits of the robots size and joint movements. For robots of polar, cylindrical, or jointed-arm configuration, the 3 degrees of freedom associated with the arm and body motions

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