Using the incomplete beta function as transfer function for dwell–rise–dwell motions

Bäsel, Uwe

doi:10.1016/j.mechmachtheory.2023.105387

Cited by 4 publications

(2 citation statements)

References 8 publications

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“…Dwells can be found in many different cam mechanisms and are a fundamental part of cam design. Dwell-rise-dwell or rise-dwell-return cams have been used in previous research to explore beta functions and their ability to approximate the motion of a pivoting cam follower [4].…”

Section: Introductionmentioning

confidence: 99%

Designing a Laboratory Cam Profile Measuring Machine to Validate Follower Displacements

Bednarz,

Abad,

Patel

et al. 2024

Hardware

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This study presents the design, build, and evaluation of a laboratory cam profile measuring machine tailored to demonstrate the mechanical principles and applications of various cam shapes. Utilizing a diverse set of cam profiles, the machine effectively converts rotational motion into measurable linear motion, achieving a range of motion profiles, including rising, declining, steady, and instantaneous actions. Key components of the machine include an angle gauge for precise rotational measurements and a linear dial indicator for accurately gauging the cam-induced displacement. This setup facilitates the measuring of displacement, and computation of velocity and acceleration for each cam shape, offering a dynamic visual and numerical aid for engineering and design.

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Section: Introductionmentioning

confidence: 99%

Designing a Laboratory Cam Profile Measuring Machine to Validate Follower Displacements

Bednarz,

Abad,

Patel

et al. 2024

Hardware

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“…The cam mechanism, as a contact-driven motion unit, plays an integral role in many modern automation machines, such as CNC machining centers [1] and internal combustion engines [2]. The distinct feature of the cam mechanism lies in its ability to tailor the cam profile using predefined transfer functions (termed as motion curves) [3], thus allowing the active control of the follower's motion to meet case-specific transmission requirements [4], as illustrated in Figure 1a. Hence, the mathematical construction and computational optimization of the motion curve have been long-standing focal points in the development of high-performance cam mechanisms.…”

Section: Introductionmentioning

confidence: 99%

An Integrated C4-Spline Interpolation and Time-Free Global Optimization Methodology Applied to High-Speed Cam Motion Design

Liu,

Xi,

Luo

et al. 2024

Machines

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The optimal tuning of high-order motion parameters has emerged as a promising strategy for actively controlling the kinematics/dynamics of high-speed cam mechanisms. However, accomplishing this task remains challenging with current low-order interpolation or tuning methods. This study proposes an integrated high-order interpolation and tuning methodology for the optimal construction of high-speed motion curves. Initially, an explicit C4-spline interpolant (C4SI) is developed. This interpolant utilizes four-order continuous (C4) splines to synthesize a high-fidelity motion curve that satisfies the predefined motion constraints up to the fourth order, including dimensionless displacement, velocity, acceleration, jerk, and quirk. Concerning the reduction of motion peaks, a unique C4SI-based global kinematics optimization strategy is designed, using the definite integral of the motion curve (free of the time variable) as the objective function. This facile time-free optimization strategy could yield a simultaneous reduction in multiple motion peaks (up to five), which is currently inaccessible with conventional motion tuning strategies. Concerning the improvement of dynamic characteristics, the C4SI-based time-free global dynamics optimization of variable motion parameters is further performed. The results indicate that the optimized fourth-order motion curve offers minimal high-speed transmission error and residual vibration over the whole rise-dwell-return-dwell cycle, which outperforms the standard motion curves and other low-order counterparts.

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Design of the high-speed cam profile for the multi-DOF follower

Han,

Huang,

2024

Proceedings of the Institution of Mechanical Engineers, Part C:

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The multi-degree-of-freedom (multi-DOF) follower may suffer from unwanted vibrations when the cam works at the high speed. The vibrations will cause significant problems of positioning accuracy, noise, wear, forces, and operating costs for the cam-follower mechanism. It is challenging to design high-speed cam profiles for multi-DOF followers because of the complicated dynamics. A novel method is presented to design the cam profile in this article. A polynomial profile filters through a continuous-piecewise smoother to produce the cam profile. While the profile and their derivatives are continuous, the profile provides good performance on the vibration reduction for multi-DOF followers. Simulated and experimental results from a flexible-link manipulator validate the effectiveness of the cam profiles created by the new method.

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Using the incomplete beta function as transfer function for dwell–rise–dwell motions

Cited by 4 publications

References 8 publications

Designing a Laboratory Cam Profile Measuring Machine to Validate Follower Displacements

Designing a Laboratory Cam Profile Measuring Machine to Validate Follower Displacements

An Integrated C4-Spline Interpolation and Time-Free Global Optimization Methodology Applied to High-Speed Cam Motion Design

Design of the high-speed cam profile for the multi-DOF follower

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