Structure of Robot Compliance

Patterson, Timothy; Lipkin, Harvey

doi:10.1115/1.2919228

Cited by 127 publications

(50 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…While searching for a 3-D analog of the center of compliance, Patterson and Lipkin [25] were the first to recognize the existence of the principal stiffness parameters. In order to provide a sense of continuity with the existing literature, we show that our principal parameters are equivalent to the ones derived by Patterson and Lipkin using screw coordinates.…”

Section: B Screw Coordinates Interpretationmentioning

confidence: 99%

“…We first identify the frame-invariant features of a grasp's stiffness matrix, in terms of invariant scalars called the principal translational and rotational stiffness parameters (Section III). These parameters were first identified by Patterson and Lipkin [25] using screw theory. The same parameters were obtained by us using a different approach, and were proven by us to have frame invariant properties.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A stiffness-based quality measure for compliant grasps and fixtures

Lin

Burdick

Rimon

2000

IEEE Trans. Robot. Automat.

View full text Add to dashboard Cite

Abstract-This paper presents a systematic approach to quantifying the effectiveness of compliant grasps and fixtures of an object. The approach is physically motivated and applies to the grasping of two-and three-dimensional objects by any number of fingers. The approach is based on a characterization of the frame-invariant features of a grasp or fixture stiffness matrix. In particular, we define a set of frame-invariant characteristic stiffness parameters, and provide physical and geometric interpretation for these parameters. Using a physically meaningful scheme to make the rotational and translational stiffness parameters comparable, we define a frame-invariant quality measure, which we call the stiffness quality measure. An example of a frictional grasp illustrates the effectiveness of the quality measure. We then consider the optimal grasping of frictionless polygonal objects by three and four fingers. Such frictionless grasps are useful in high-load fixturing applications, and their relative simplicity allows an efficient computation of the globally optimal finger arrangement. We compute the optimal finger arrangement in several examples, and use these examples to discuss properties that characterize the stiffness quality measure.

show abstract

Section: B Screw Coordinates Interpretationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A stiffness-based quality measure for compliant grasps and fixtures

Lin

Burdick

Rimon

2000

IEEE Trans. Robot. Automat.

View full text Add to dashboard Cite

show abstract

“…In the planar case, the alternative approach yields a formula for that contains the term , the radius of curvature of the compressed object at the contact, and the term . The formula for using the alternative approach is (26) But and . Hence, (26) is identical to (11).…”

Section: Proof Of Proposition 44mentioning

confidence: 99%

“…Compliance typically appears in these applications as a design parameter which is implemented by various stiffness-control methods [1], [7], [12], [25], [26], [34]. The stiffness-control approach is fully justified in multifinger grasps where compliance introduced at the finger joints dominates the natural compliance at the fingertips.…”

mentioning

confidence: 99%

Computation and Analysis of Natural Compliance in Fixturing and Grasping Arrangements

Lin

Burdick²,

Rimon³

2004

IEEE Trans. Robot.

View full text Add to dashboard Cite

Abstract-This paper computes and analyzes the natural compliance of fixturing and grasping arrangements. Traditionally, linear-spring contact models have been used to determine the natural compliance of multiple contact arrangements. However, these models are not supported by experiments or elasticity theory. We derive a closed-form formula for the stiffness matrix of multiple contact arrangements that admits a variety of nonlinear contact models, including the well-justified Hertz model. The stiffness matrix formula depends on the geometrical and material properties of the contacting bodies and on the initial loading at the contacts. We use the formula to analyze the relative influence of first-and second-order geometrical effects on the stability of multiple contact arrangements. Second-order effects, i.e., curvature effects, are often practically beneficial and sometimes lead to significant grasp stabilization. However, in some contact arrangements, curvature has a dominant destabilizing influence. Such contact arrangements are deemed stable under an all-rigid body model but, in fact, are unstable when the natural compliance of the contacting bodies is taken into account. We also consider the combined influence of curvature and contact preloading on stability. Contrary to conventional wisdom, under certain curvature conditions, higher preloading can increase rather than decrease grasp stability. Finally, we use the stiffness matrix formula to investigate the impact of different choices of contact model on the assessment of the stability of multiple contact arrangements. While the linear-spring model and the more realistic Hertz model usually lead to the same stability conclusions, in some cases, the two models lead to different stability results.

show abstract

“…The standard way to determine if a symmetric matrix is positive definite is to check that all it's leading minors are positive, see [2, Another characterisation of 6 × 6 positive definite symmetric matrices is due to Patterson and Lipkin [5]. This involves a slightly different eigenvalue problem.…”

Section: Over Dampingmentioning

confidence: 99%

Theory of vibrations in Stewart platforms

Selig

Ding²

Proceedings 2001 IEEE/RSJ International Conference on Intelligent Robots and Systems. Expanding the Societal Role of Robotics I

View full text Add to dashboard Cite

This article develops a simple linear model for the motion of a Stewart platform in a stationary position. That is, the situation where the platform is at rest and is then subject to an impulsive disturbance. The hydraulic actuators are modelled as simple spring-dashpot systems and the stiffness and damping matrices of the system are derived. It is found that the damping and stiffness matrices are simply proportional to each other and this simplifies the dynamics greatly. The general solution to the equations of motion is a linear combination of eigensolutions. The eigensolutions are damped oscillations about the harmonic screws of the undamped system. The characteristic values associated with each eigensolution can also be found in terms of the undamped frequencies. Finally some remarks are made concerning the possibility of the system being fully damped.

show abstract

Structure of Robot Compliance

Cited by 127 publications

References 0 publications

A stiffness-based quality measure for compliant grasps and fixtures

A stiffness-based quality measure for compliant grasps and fixtures

Computation and Analysis of Natural Compliance in Fixturing and Grasping Arrangements

Theory of vibrations in Stewart platforms

Contact Info

Product

Resources

About