Huimin Dong

Kinematic Fundamentals of Planar Harmonic Drives

This paper presents the kinematic model and offers a rigorous analysis and description of the kinematics of planar harmonic drives. In order to reflect the fundamental kinematic principle of harmonic drives, the flexspline of a harmonic drive is assumed to be a ring without a cup. A tooth on the flexspline is a rigid body, and the motion of the tooth is fully governed by the wave generator and the nominal transmission ratio of the harmonic drive. The proposed model depicts the flexspline tooth and the wave generator as a cam-follower mechanism, with the follower executing a combined translating and oscillating motion. With the rigid tooth motion obtained, the conjugate condition between the flexspline and the circular spline is determined, from which the conjugate tooth profile can be derived. In this paper, the motion is governed by geometry, and the flexibility of the flexspline only serves as a spring to maintain the contact between the cam and the follower. For any wave generator and any transmission ratio, the explicit expression of the conjugate condition is presented. For a given circular or flexspline tooth profile, the exact conjugate tooth profile can be obtained. The phenomenon of twice engagement is discussed for the first time.

Differential Contact Path and Conjugate Properties of Planar Gearing Transmission

This paper presents a general conjugation model based on the intrinsic kinematical properties of the contact path. The model is truly general for any planar transmission through contact curves, such as gearing. The effectiveness of the method is not affected by the type of centrodes or motion and path of contact. With the method, for any given centrodes and any chosen path of contact, the corresponding conjugate curves can be identified and the geometric properties of the conjugation can be determined even before the conjugate curves are found. The method is demonstrated with straight, circular, and polynomial paths of contact in both circular and noncircular gears. The versatility of the theory and the outstanding features of the method become obvious with treating arbitrary centrodes or any planar motion transmission. The freedom of selecting contact path suggests the possibility of optimal conjugation design.

A Unified Formulation for Dimensional Synthesis of Stephenson Linkages

The unified formulation of dimensional synthesis of Stephenson linkages for motion generation is the subject of this paper. Burmester theory is applied to the six-bar linkage, which leads to a unified formulation applicable for all three types of Stephenson linkages. This is made possible by virtue of parameterized position vectors, which simplify the formulation of synthesis equations. A design example is included to demonstrate the application of the method developed. [DOI: 10.1115/1.4032701]

Dynamic Modeling of Planetary Gear Train for Vibration Characteristic Analysis

In this paper, a torsional-translational coupled nonlinear dynamic model for planetary gear train with three planet gears is developed to investigate its vibration characteristic. In this lumped-parameter model, gears and carrier all have three degrees of freedom: two translations and one rotation. The equations of motion of the dynamic model are built in consideration of gear elastic deformation and time-varying mesh stiffness. Gear elastic compatibility equations are developed to describe the relationship between displacements, elastic deformations and transmission errors. Thus, dynamic equations of the planetary gear train consist of equations of motion and gear elastic compatibility equations can be found and the effects of support stiffness and flexible planet pin on vibration characteristic have been addressed. The results show floating central gear and flexible planet pin can avoid critical operating conditions, which provides a theoretical guideline for the design of planetary gear train.

A novel accuracy model for the intrinsic kinematic property of a prismatic pair

A novel accuracy model is proposed to analyze the intrinsic kinematic property of the prismatic pair. The geometric error of guide rails, the elastic constrained structure of moving joints, and fixed joints are considered synthetically. The geometric error is measured by the 5D laser interferometer system with slide blocks. The elastic moving joints are equivalent to the springs, while the fixed joints to contact layers. The equilibrium equations are then set up and the analytical solution for five degrees-of-freedom errors of the moving table is revealed. The global invariant errors, including the straightness error space and the spherical image error surface, are proposed to describe the global kinematic characteristic of the moving table. Along with the comparison between the measured and theoretical indicators, the verification experiment to prove the availability of the model is carried out. As the movement of the table can be forecast precisely and evaluated objectively, the new methodology provides a theoretical basis for machine tool manufacture.

A new approach of kinematic geometry for error identification and compensation of industrial robots

A new approach for kinematic calibration of industrial robots, including the kinematic pair errors and the link errors, is developed in this paper based on the kinematic invariants. In most methods of kinematic calibration, the geometric errors of the robots are considered in forms of variations of the link parameters, while the kinematic pairs are assumed ideal. Due to the errors of mating surfaces in kinematic pairs, the fixed and moving axes of revolute pairs, or the fixed and moving guidelines of prismatic pairs, are separated, which can be concisely identified as the kinematic pair errors and the link errors by means of the kinematic pair errors model, including the self-adaption fitting of a ruled surface, or the spherical image curve fitting and the striction curve fitting. The approach is applied to the kinematic calibration of a SCARA robot. The discrete motion of each kinematic pair in the robot is completely measured by a coordinate measuring machine. Based on the global kinematic properties of the measured motion, the fixed and moving axes, or guidelines, of the kinematic pairs are identified, which are invariants unrelated to the positions of the measured reference points. The kinematic model of the robot is set up using the identified axes and guidelines. The results validate the approach developed has good efficiency and accuracy.

A Novel Kinematic Model of Spatial Four-bar Linkage RSPS for Testing Accuracy of Actual R-Pairs with Ball-bar

A novel kinematic model of spatial four-bar linkage RSPS is firstly presented for accuracy testing of R-pairs. During accuracy testing, the kinematic chain SPS of the ball bar and the R-pair constitute a RSPS mechanism, while the structure parameters of the RSPS mechanism correspond to the mounting parameters of the ball bar. Thus, the mounting position errors of the ball bar are identified by using the kinematic synthesis of the RSPS mechanism, based on the discrete data measured by the ball bar. Furthermore, the relationships between the measured errors and the mounting parameters of the ball bar are analyzed, by using the solutions of the kinematic equations of the RSPS mechanism.