Comments on “The Principal Axes Decomposition of Spatial Stiffness Matrices”

A significant amount of research has been directed toward developing a more intuitive appreciation of spatial elastic behavior. Results of these analyses have been described in terms of behavior decompositions and in terms of behavior centers. In a recent paper entitled “The Principal Axes Decomposition of Spatial Stiffness Matrices” by Chen et al. (IEEE Trans. Robot., vol. 31, no. 1, pp. 191-207), a decomposition of spatial stiffness was presented, and centers of stiffness and compliance were identified. The results presented in the paper have substantial overlap with previously published results and redefine previously used terms. The objective of this communication is to clarify the contributions of prior work and to standardize the terminology used in describing spatial elastic behavior

Geometric Construction-Based Realization of Spatial Elastic Behaviors in Parallel and Serial Manipulators

This paper addresses the realization of spatial elastic behavior with a parallel or a serial manipulator. Necessary and sufficient conditions for a manipulator (either parallel or serial) to realize a specific elastic behavior are presented and interpreted in terms of the manipulator geometry. These conditions completely decouple the requirements on component elastic properties from the requirements on mechanism kinematics. New construction-based synthesis procedures for spatial elastic behaviors are developed. With these synthesis procedures, one can select each elastic component of a parallel (or serial) mechanism based on the geometry of a restricted space of allowable candidates. With each elastic component selected, the space of allowable candidates is further restricted. For each stage of the selection process, the geometry of the remaining allowable space is described

Accuracy Improvement for Stiffness Modeling of Parallel Manipulators

The paper focuses on the accuracy improvement of stiffness models for parallel manipulators, which are employed in high-speed precision machining. It is based on the integrated methodology that combines analytical and numerical techniques and deals with multidimensional lumped-parameter models of the links. The latter replace the link flexibility by localized 6-dof virtual springs describing both translational/rotational compliance and the coupling between them. There is presented detailed accuracy analysis of the stiffness identification procedures employed in the commercial CAD systems (including statistical analysis of round-off errors, evaluating the confidence intervals for stiffness matrices). The efficiency of the developed technique is confirmed by application examples, which deal with stiffness analysis of translational parallel manipulators

Personalised 3D knee compliance from clinically viable knee laxity measurements: A proof of concept ex vivo experiment.

Personalised information of knee mechanics is increasingly used for guiding knee reconstruction surgery. We explored use of uniaxial knee laxity tests mimicking Lachman and Pivot-shift tests for quantifying 3D knee compliance in healthy and injured knees. Two healthy knee specimens (males, 60 and 88 years of age) were tested. Six-degree-of-freedom tibiofemoral displacements were applied to each specimen at 5 intermediate angles between 0° and 90° knee flexion. The force response was recorded. Six-degree-of-freedom and uniaxial tests were repeated after sequential resection of the anterior cruciate, posterior cruciate and lateral collateral ligament. 3D knee compliance (C6DOF) was calculated using the six-degrees-of-freedom measurements for both the healthy and ligament-deficient knees and validated using a leave-one-out cross-validation. 3D knee compliance (CCT) was also calculated using uniaxial measurements for Lachman and Pivot-shift tests both conjointly and separately. C6DOF and CCT matrices were compared component-by-component and using principal axes decomposition. Bland-Altman plots, median and 40-60th percentile range were used as measurements of bias and dispersion. The error on tibiofemoral displacements predicted using C6DOF was < 9.6% for every loading direction and after release of each ligament. Overall, there was good agreement between C6DOF and CCT components for both the component-by-component and principal component comparison. The dispersion of principal components (compliance coefficients, positions and pitches) based on both uniaxial tests was lower than that based on single uniaxial tests. Uniaxial tests may provide personalised information of 3D knee compliance

Explicit robust schemes for implementation of a class of principal value-based constitutive models: Theoretical development

The issue of developing effective and robust schemes to implement a class of the Ogden-type hyperelastic constitutive models is addressed. To this end, explicit forms for the corresponding material tangent stiffness tensors are developed, and these are valid for the entire deformation range; i.e., with both distinct as well as repeated principal-stretch values. Throughout the analysis the various implications of the underlying property of separability of the strain-energy functions are exploited, thus leading to compact final forms of the tensor expressions. In particular, this facilitated the treatment of complex cases of uncoupled volumetric/deviatoric formulations for incompressible materials. The forms derived are also amenable for use with symbolic-manipulation packages for systematic code generation