China
Africa
Explore chapters and articles related to this topic
Control and Manipulation
Published in Marina Indri, Roberto Oboe, Mechatronics and Robotics, 2020
Bruno Siciliano, Luigi Villani
The design of the interaction control and the performance analysis are usually carried out under simplifying assumptions. The following two cases are considered: The robot and the environment are perfectly rigid, and purely kinematics constraints are imposed by the environment, known as holonomic constraints.the robot—rigid or elastic—interacts with a passive environment.
Hand Dynamics and Control
Published in Richard M. Murray, Zexiang Li, S. Shankar Sastry, A Mathematical Introduction to Robotic Manipulation, 2017
Richard M. Murray, Zexiang Li, S. Shankar Sastry
The constraint in equation (6.1) is an example of a holonomic constraint. More generally, a constraint is said to be holonomic if it restricts the motion of the system to a smooth hypersurface in the (unconstrained) configuration space Q. Holonomic constraints can be represented locally as algebraic constraints on the configuration space, hi(q)=0,i=1,…,k. Each hi is a mapping from Q to ℝ which restricts the motion of the system. We assume that the constraints are linearly independent and hence the matrix ∂h∂q=[∂h1∂q1⋯∂h1∂qn⋱∂hk∂q1⋯∂hk∂qn] is full row rank. (In the classical mechanics literature, constraints of the form in equation (6.2) are sometimes referred to as scleronomic constraints. Holonomic and scleronomic come from Greek and mean respectively “all together lawful” and “rigid” respectively. Time-varying constraints on q are called rheonomic, for “flowing.” We will not use the terms scleronomic and rheonomic in this book, only the term holonomic.)
Parallel manipulator domains of singularity free functionality
Published in Mechanics Based Design of Structures and Machines, 2021
As shown schematically in Figure 1, the mechanical component of a parallel manipulator is a mechanism, whose configuration is defined by generalized coordinates that are subject to m holonomic constraints, where is continuously differentiable. There are many choices for generalized coordinates that specify the configuration of a mechanism, independent of any concept of input or output and control of the mechanism, any of which may be employed in the present formulation. As commonly used in the mechanical systems literature, such generalized coordinates are not independent; i.e., they must satisfy holonomic constraints of Eq. (3). A key requirement of generalized coordinates and the associated constraints of Eq. (3) is that the constraint Jacobian have full row rank, in which case the mechanism has degrees of freedom in a neighborhood of q; i.e., degree of freedom is a local property of the mechanism. In such neighborhoods, the implicit function theorem (Corwin and Szczarba 1982) shows that a nonsingular configuration can be uniquely defined by k of the n generalized coordinates or by another choice of k variables.
Muscle co-contraction in an upper limb musculoskeletal model: EMG-assisted vs. standard load-sharing
Published in Computer Methods in Biomechanics and Biomedical Engineering, 2021
Ehsan Sarshari, Matteo Mancuso, Alexandre Terrier, Alain Farron, Philippe Mullhaupt, Dominique Pioletti
A shoulder and elbow musculoskeletal model was developed from MRI scans of the same subject (Figure 2(a)) (Ingram 2015; Ingram et al. 2016; Sarshari 2018). It consisted of six rigid bodies including thorax, clavicle, scapula, humerus, ulna, and radius. It had nine degrees of freedom (DOF) attributing to three ball-and-socket joints associating with sternoclavicular (SC), acromioclavicular (AC), and glenohumeral (GH) joints and two hinge joints for humeroulnar (HU) and radioulnar (RU) joints and two holonomic constraints (Figure 2(b)). Two constraints namely and restricted trigonum scapulae (TS) and angulus inferior (AI) respectively on the scapula medial boarder to glide over two ellipsoids approximating the thorax and the underlying soft tissues. The ISB recommendations (International Society of Biomechanics, 2005) were followed to define six bone-fixed frames. A generalized coordinate vector () was considered to define the upper extremity configuration. The forward kinematic map (ξ) was developed to define the inertial coordinate of the bony landmark () associated with the generalized coordinates at time t (Appendix A.1).
Well posed formulations of holonomic mechanical system dynamics and design sensitivity analysis
Published in Mechanics Based Design of Structures and Machines, 2020
For purposes of this paper, a mechanical system is defined as a collection of rigid bodies whose position and orientation relative to an inertial reference frame are defined by generalized coordinates that satisfy holonomic constraints, where is a vector of problem data, or design variables, that do not depend on time and define the geometry and kinetic properties of the system. Time independent constraints are treated here, but the formulation is extended to time dependent constraints in (Haug 2016a, 2019). With differentiating Eq. (1) with respect to time yields velocity and acceleration constraints, where a bold symbol is a vector or matrix, an over dot denotes derivative with respect to time, an over tilde (hat) identifies a variable that is held constant for the indicated differentiation, and the multivariable calculus notation is used. It is important that the Jacobian of the holonomic constraints of Eq. (1) has full row rank, for all q in neighborhoods of and of b. Otherwise the constraints are dependent, or at least locally singular.