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Kinematic Analysis of Planar Mechanisms
Published in Kevin Russell, Qiong Shen, Raj S. Sodhi, Kinematics and Dynamics of Mechanical Systems Implementation in MATLAB® and Simmechanics®, 2018
Kevin Russell, Qiong Shen, Raj S. Sodhi
Another use for ICs for the planar four-bar mechanism (particularly I1–3) is to replicate the motion of the coupler link. Because the locations of ICs vary with the position of the mechanism, a locus of ICs can be produced over a crank rotation range. A locus of ICs is called a centrode. Figure 4.11a illustrates the centrode produced for a given Grashof triple-rocker mechanism. The centrode produced for a given mechanism is called a fixed centrode because it is stationary. Figure 4.11b illustrates the centrode produced for the inverted triple-rocker mechanism. In this particular inversion, the coupler becomes the ground and the ground becomes the coupler (see Figure 3.13). The centrode produced for an inverted mechanism is called a moving centrode because this centrode can exhibit motion—specifically, rolling motion—over the fixed centrode.
Planar Kinematics of Rigid Bodies
Published in Asok Kumar Mallik, Amitabha Ghosh, Günter Dittrich, Kinematic Analysis and Synthesis of Mechanisms, 1994
Asok Kumar Mallik, Amitabha Ghosh, Günter Dittrich
The instantaneous center of velocity of a moving rigid body is, as the name implies, applicable at an instant, i.e., for a given position or configuration of the moving body. As the rigid body moves, the locus of the instantaneous center on the fixed reference plane is termed the fixed centrode. The locus of the instantaneous center on the moving body is called the moving centrode. We shall denote the fixed and moving centrodes by Cf and Cm, respectively. Consider the motion of a circular wheel that rolls without slipping on a fixed, horizontal surface (Fig. 2.8-1). The instantaneous center of velocity I12 is always at the point of contact between the wheel and the surface (refer to Section 2.6). Thus, as the wheel moves on, the locus of I12 on the fixed body 1 is obviously the line Cf, and that on wheel 2 is the periphery of the wheel, Cm. For better appreciation of the role of centrodes in the kinematic analysis and synthesis of planar linkages, we shall first develop some concepts associated with finite displacements of a rigid body.
A New Mathematical Model for the Human Ankle Joint
Published in J. Middleton, M. L. Jones, G. N. Pande, Computer Methods in Biomechanics & Biomedical Engineering – 2, 2020
A. Leardini, J.J. O’Connor, F. Catani
An important property of the linkage is that the point at which the two ligaments cross (point I in figure 2) is the instant centre of the joint, i.e. the instant point of zero velocity of the talus/calcaneus rotation relative to the tibia/fibula segment. The path of the instantaneous positions of the centre of rotation is the so-called ‘centrode’ of the linkage. The flexion axis of the joint passes through I.
Towards optimal toe-clearance in synthesizing polycentric prosthetic knee mechanism
Published in Computer Methods in Biomechanics and Biomedical Engineering, 2022
Initially, the cosmetically acceptable linkage dimensions are arbitrarily chosen (Chauhan and Bhaduri 2011) and the base and coupler link angles are assumed. The x/y ratio at heel contact and push-off are obtained using CAD drawing of the linkages. Once the stability criterion is satisfied, the mechanism is constructed using the GIM software. There, the fixed centrode, moving centrode and centrode tangent of the mechanism are extracted. The centrodes are verified for approximately same initial curvature (Hobson and Torfason 1974) and steepness, the ICR curve for the selected linkages are compared, and the best linkage is selected for further analysis using SAM (Simulation and Analysis of Mechanisms) and optimization (Krishnaraju and Zubar 2021). The Figure 4 sows the configuration of the four-bar mechanism.