Multibody in Human Modelling and Biorobotics Flashcards

Flashcards covering the Multibody in Human Modelling and Biorobotics lecture handbook.

What is the definition of a robot according to the handbook?

An embodied agent capable of performing physical tasks by integrating sensing, computation, and actuation.

In Greek mythology (~ 1000 BC), who was the giant bronze automaton created to protect Europa in Crete?

Talos

What early automata were documented by Hero of Alexandria around 300 BC – 100 AD?

Coin-operated machines, a wind-powered organ, and a steam-powered device (rocket-type engine).

In which sheet of Leonardo da Vinci's Codex Atlanticus are the mechanical details for a drumming robot documented?

Codex Atlanticus sheet f.579r

What is René Descartes' 17th-century philosophical notion comparing animal behavior to mechanical function?

Animal machine

Who introduced the word 'robot' in his 1920 science fiction play R.U.R. (Rossum's Universal Robots)?

Karel Čapek

What was the name of the first industrial robot deployed on a General Motors assembly line in the 1950s?

Unimate

Who is considered the father of multi-body dynamics through his formulation in the 1788 treatise Mécanique Analytique?

Joseph-Louis Lagrange

Who originally developed the computer program ADAMS for numerical simulation of multibody 3D systems in his 1973 Ph.D. thesis?

Nicolae Orlandea

How many degrees of freedom (DOFs) does an unconstrained rigid body possess in three-dimensional Euclidean space?

$6 \text{ DOFs}$ (3 translations and 3 rotations)

In rigid body kinematics, what two fundamental properties collectively define the 'pose' of a body?

Position and orientation

To which mathematical group do 3D rotation matrices belong?

Special Orthogonal group $SO(3)$

What key mathematical property of 3D rotation matrices $R$ makes computing their inverse computationally efficient?

The inverse is equal to its transpose ($R^{-1} = R^T$)

What mechanical and mathematical phenomenon causes the loss of one degree of freedom in three-angle orientation representations when two rotation axes align?

Gimbal lock

How many parameters are used in unit quaternions (Euler parameters) to describe orientation without singularities?

$4 \text{ parameters}$ subject to a unity norm constraint ($\eta^2 + \boldsymbol{\varepsilon}^T \boldsymbol{\varepsilon} = 1$)

What are the matrix dimensions of a standard homogeneous transformation matrix $T_j^i$?

$$4 \times 4$$

According to the Tennis Racket Theorem, rotations around which principal axes of inertia are dynamically stable?

The principal axes corresponding to the minimum and maximum moments of inertia

What is the key distinction between lower pair joints and higher pair joints in kinematics?

Lower pairs connect along sliding surfaces; higher pairs connect at a point or a line.

In a screw pair (helical joint), how is translational displacement $d$ coupled to rotation angle $\vartheta$?

$d = h\vartheta$, where $h$ is the pitch of the screw

How many degrees of freedom (DOFs) does a spherical kinematic pair permit?

$3 \text{ DOFs}$ (independent rotations about three axes)

How many total degrees of freedom does a planar kinematic pair possess?

$3 \text{ DOFs}$ (two independent translations and one rotation in a plane)

What is the structural difference between serial and parallel robot manipulators?

Serial manipulators have links arranged in an open chain; parallel manipulators have multiple independent chains connecting the base to the end-effector simultaneously.

In robotics reference frame conventions, which frame is attached to the nonmoving base structure (link 0)?

Base frame ($\{B\}$)

What letter sequence denotes a Cartesian manipulator based on the kinematic nature of its first three joints?

$TTT$ (three mutually orthogonal prismatic joints)

What does the abbreviation SCARA stand for in robotics?

Selectively Compliant Assembly Robot Arm

Who introduced the Denavit-Hartenberg (D-H) method in their landmark 1955 paper?

Jacques Denavit and Richard Hartenberg

What four scalar parameters characterize each link in the Denavit-Hartenberg (D-H) convention?

Link length ($a_i$), link twist ($\alpha_i$), link offset ($d_i$), and joint angle ($\vartheta_i$)

In the Denavit-Hartenberg (D-H) convention, how is the $z_i$-axis of link frame $\{i\}$ aligned?

Aligned with the axis of Joint $i + 1$

In the Denavit-Hartenberg (D-H) convention, along what line is the $x_i$-axis directed?

Along the mutual perpendicular pointing from $z_{i-1}$ toward $z_i$

What is the Grübler-Kutzbach equation used to calculate the mobility $M$ of a planar closed-chain mechanism?

$M = 3(n - 1) - 2J - H$ (where $n$ is the number of links, $J$ is lower pair joints, and $H$ is higher pair joints)

In kinematic mobility analysis, what does a calculated mobility value of $M < 0$ indicate?

The system is over-constrained, or hyperstatic

What are the inputs and outputs of the forward kinematics problem in serial robot manipulators?

Input: joint variables vector $\mathbf{q}$; Output: position and orientation (pose) of the end-effector

In robot workspace analysis, how does the dextrous workspace differ from the reachable workspace?

Reachable workspace includes all positions the end-effector can attain in any orientation; dextrous workspace includes only positions where the end-effector can attain any desired orientation.

What are the inputs and outputs in inverse dynamics analysis of serial chains?

Inputs: motion trajectory (positions, velocities, accelerations) and external forces; Outputs: required joint forces and torques

By modeling convention, under what deformation conditions are translational spring restoring forces considered positive vs negative?

Positive under compression, negative under traction

What is the equivalent stiffness $k_{eq}$ for two linear springs with stiffnesses $k_1$ and $k_2$ connected in parallel?

$$k_{eq} = k_1 + k_2$$

What is the equivalent stiffness $k_{eq}$ for two linear springs with stiffnesses $k_1$ and $k_2$ connected in series?

$$k_{eq} = \frac{k_1 k_2}{k_1 + k_2}$$

In the 1D ligament model by Blankevoort et al. (1991), what equation defines the force-strain relationship in the linear region ($\varepsilon > 2\varepsilon_L$)?

$$F = -k(\varepsilon - \varepsilon_L)$$

What empirical reference strain value $\varepsilon_L$ is assumed in the Blankevoort et al. (1991) 1D ligament model?

$$\varepsilon_L = 0.03$$

What mathematical formula gives the restoring force $F$ of a linear translational damper with damping coefficient $c$?

$$F = c(\dot{x}_1 - \dot{x}_2) = c \Delta \dot{x}$$

In multibody dynamics, what matrix dimensions define the stiffness and damping properties of a 6-component bushing element?

A $6 \times 6$ stiffness matrix and a $6 \times 6$ damping matrix

How can a bushing element be repurposed as a compliant motion agent to drive motion in a multibody model?

By connecting the real body to a 'dummy' body following a prescribed trajectory via a bushing element

What is the general mathematical formula for the control action $A(t)$ produced by a Proportional-Integral-Derivative (PID) controller?

$$A(t) = K_p e(t) + K_i \int_0^t e(\tau)\,d\tau + K_d \frac{de(t)}{dt}$$

In a PID control loop, what specific physical behaviors do gains $K_p$, $K_i$, and $K_d$ represent?

$K_p$ acts as a spring (proportional to error), $K_i$ eliminates steady-state error (accumulates error history), and $K_d$ acts as a damper (proportional to error velocity).

In the Ziegler-Nichols empirical tuning method, what formula sets the proportional gain $K_p$ for a full PID controller given ultimate gain $K_u$?

$$K_p = 0.60 K_u$$

In a simplified Hill-type muscle model, how is maximum isometric force $F_{max}$ calculated?

$F_{max} = \sigma_{max} \cdot PCSA$ (where $\sigma_{max}$ is maximum muscle stress and $PCSA$ is physiological cross-sectional area)

What distinguishes intermittent (impact) contact from persistent (static) contact in multibody systems?

Intermittent contact occurs for short periods where bodies collide and separate; persistent contact occurs over long periods where relative separation velocity is near zero.

In contact modeling, what is the fundamental difference between the piecewise approach and the continuous approach?

The piecewise approach assumes instantaneous impact using momentum balance; the continuous approach resolves motion during local interpenetration (deformation).

In Hertz's contact theory for two elastic spheres or a sphere and a plane, what exponent $e$ is applied to penetration depth $\delta$?

$e = 1.5$ (giving $F_c = K \delta^{1.5}$)

How does the Hunt-Crossley impact contact model avoid non-physical negative contact forces during separation?

By making the damping coefficient $C(\delta)$ dependent on penetration depth $\delta$, so damping vanishes as penetration goes to zero.

What two distinct friction regimes are defined in Coulomb's friction model?

Static (stiction) friction when relative velocity is zero ($v_t = 0$), and dynamic (sliding) friction when relative velocity is non-zero ($v_t \neq 0$)

In MSC Adams, which solver integrator is specifically recommended for contact models because it monitors velocity integration errors and prevents acceleration spikes?

SI2 integrator

In discrete parametric design studies, how is approximate design sensitivity $S_i$ formulated?

$$S_i = \frac{1}{2} \left( \frac{O_{i+1} - O_i}{V_{i+1} - V_i} + \frac{O_i - O_{i-1}}{V_i - V_{i-1}} \right)$$

What formula gives the total number of trial combinations in a full-factorial Design of Experiments (DoE) with $m$ levels and $n$ factors?

$$m^n$$

In a Latin square Design of Experiments matrix with $n$ levels, how many total simulation trials are required?

$n^2$ trials

What does the abbreviation ANCF stand for in the context of FE Parts in flexible multibody dynamics?

Absolute Nodal Coordinate Formulation

In the Floating Frame of Reference (FFR) formulation, how is the total motion of a point on a flexible body decomposed?

Into large rigid-body motion of a local floating frame and small elastic deformation relative to that floating frame

What two sets of mode shapes form the modal basis in the Craig-Bampton Component Mode Synthesis method?

Constraint modes (for boundary degrees of freedom) and fixed-boundary normal modes (for interior degrees of freedom)

Why is data filtering or smoothing required before performing numerical differentiation on raw experimental kinematic signals?

Because numerical differentiation amplifies high-frequency noise and small discontinuities in the signal, producing corrupted velocity and acceleration profiles.

What is the primary difference between Hardware-in-the-Loop (HIL) and Software-in-the-Loop (SIL) simulation methodologies?

HIL integrates real physical hardware components into a real-time virtual simulation loop; SIL tests embedded control software entirely within a virtual environment.