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Introduction
Published in Asok Kumar Mallik, Amitabha Ghosh, Günter Dittrich, Kinematic Analysis and Synthesis of Mechanisms, 1994
Asok Kumar Mallik, Amitabha Ghosh, Günter Dittrich
We have already seen that revolute and prismatic pairs are the basic building blocks of all lower pairs. All other lower pairs can be thought of as combinations of these two pairs. Moreover, a planar linkage consists of only these two types of kinematic pairs. In this section, it will be pointed out that a prismatic pair can always be thought of as the limit of a revolute pair. To demonstrate this, let us first consider a curved slider connection between two links 1 and 4 of a mechanism, as shown in Fig. 1.6-1a. A little thought would convince us that this connection is a revolute pair, since the pair variable describing the relative movement between 1 and 4 is still an angle. Hence, this mechanism can be represented by the kinematic diagram of a 4R planar linkage shown in Fig. 1.6-1b. If the radius of curvature (ρ) of the path of point B becomes infinitely large, the pair variable transforms from angular movement to linear displacement. Consequently, the connection between links 1 and 4 becomes a prismatic pair. Following this line of argument, as explained in Figs. 1.6-2a and 1.6-2b, a slider-crank mechanism is obtained as the limit of a 4R planar linkage when one revolute pair moves to infinity. Notice that the revolute pair moves to infinity along a direction perpendicular to that of the slider movement.
Kinematic Design
Published in Richard Leach, Stuart T. Smith, Basics of Precision Engineering, 2017
9. A four-bar linkage, as shown in Figure 6.55, has a driver link MN, a follower link OP and a coupler or connecting link NO. The points M, N, O and P represent revolute or pin joints. The fourth linkage is the base MP and can be referred to as the frame link or reference. Consider Figure 6.56, which shows a kinematic diagram of a planar four-bar linkage, representing the geometry of the linkage in xy coordinate system. Given that MN = 4 cm, OP = 10 cm, NO = 16 cm and MP = 14 cm, determine:
Mechanical Systems
Published in Ramin S. Esfandiari, Bei Lu, Modeling and Analysis of Dynamic Systems, 2018
To derive the differential equation of motion correctly, we recommend drawing two diagrams before applying the force and moment equations. One is the free-body diagram that shows all external forces and moments applied to the system, and the other is the kinematic diagram that indicates the acceleration at the mass center of each mass. The left-hand sides of the force and moment Equations 5.42 and 5.43 are written based on the free-body diagram, and the right-hand sides are written based on the kinematic diagram.
Area Design of Keyboard Layout for Comfortable Texting Ability with the Thumb Jacobian Matrix
Published in International Journal of Human–Computer Interaction, 2022
Le Xiong, Chenglong Fu, Shiming Deng
To evaluate quantitatively the manipulation ability of human thumb, we give the kinematic diagram of the motion mechanism of human thumb as shown in Figure 1(c). Let be a base coordinate frame fixed relative to the palm, its origin O coincides with the intersection of two orthogonal rotation axes of the compound joint CMC of the thumb, and its Z-axis overlaps with the thumb abduction/adduction axis in the palmar plane. In the thumb initial configuration, the thumb is completely adducted so that it is placed in the palmar plane spanned by the X- and Z-axes. Choose a coordinate frame fixed relative to the base of the first metacarpal bone, and it shares the same origin O and Z-axis with the coordinate frame . When the thumb abducts from its initial position (X-axis) to the current position (-axis), we also say that the coordinate frame rotates around the Z-axis. Let , and be the lengths of the 1st metacarpal bone, proximal phalange, and distal phalange of the thumb, respectively. Let the rotation angles around the CMC flexion/extension, MCP, and IP joints be , , and , respectively, then the thumb tip position coordinates , , and relative to the palm coordinate frame can be represented as