{"id":"04c67f47-b6a7-4e85-9b85-a3b35feab4e5","arxiv_id":"2506.10034","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":3.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":5,"one_line_summary":"Numerical case studies of multibody impacts with elastic supports show that impulse-momentum methods fail to handle multiple rebounds, while softer contact springs increase rebound count without changing overall motion.","lead":"This paper studies how collisions between multibody robots and flexible structures should be modeled, focusing on multiple contact points and repeated rebounds. Numerical simulations show that standard rigid-body impact methods become impractical when the struck structure vibrates, and that contact stiffness mostly changes the number of rebounds.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Section 8's broad claims that soft-contact models are problematic and that impact-momentum methods are impractical rest on an undamped three-mass chain; realistic damping or distributed flexibility may eliminate the stiffness-sensitive multi-rebounds and the duration-frequency relationship.","rationale":"The paper is best read as a numerical exploration of an undamped lumped model, not as a general proof about multibody impacts with deformable structures. The reader's weakest_assumption identifies exactly this: the three-mass spring chain with a unilateral linear spring and no damping is the only evidence for the multi-rebound behavior and the duration-frequency relationship. I agree with that assessment. The most load-bearing concern is that the central claims in Section 8—that soft-contact models are problematic and that impact-momentum methods are impractical—are extrapolated from a model that lacks dissipation and distributed flexibility, both of which are physically central to cables and branches. The paper explicitly states the springs have no damping, so the sequence of up to 9 rebounds is at least partly a consequence of a conservative system; with realistic damping, the number of rebounds would shrink and could become insensitive to contact stiffness, directly undermining the 'problematic' claim. The 'impractical' claim about rigid impulse methods is also too broad because modern nonsmooth dynamics does not require resolving each rebound by stop/restart. No code or data is provided, so these numerical results are not independently checkable, which further limits the strength of the conclusions. Because the reader already conditioned acceptance on more cautious framing and reproducibility, my concern does not change the verdict; it reinforces it. I would keep the conditional verdict and require the authors to either add the damping/distributed-parameter sensitivity study or restrict the conclusions to the tested undamped lumped model.","tokens_in":14414,"tokens_out":5432,"duration_ms":56090,"concrete_test":"Run the Section 7 benchmark with the same geometry and parameters but add proportional damping to the three-mass chain, e.g., Rayleigh damping C = αM + βK with modal damping ratios of 1% and 5% for the first two modes, across the three stiffness ratios c13 = cref, 10·cref, and 100·cref. Count the number of unilateral-spring recontacts and measure the total in-touch duration. If, at 5% damping, the system exhibits at most one or two recontacts and the in-touch duration no longer equals roughly half the period of the slowest mode, then the Section 8 conclusions are artifacts of the undamped model and should be restricted to purely elastic lumped systems.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central conclusion in Section 8 ('The application of the soft contact model is also problematic' and the claim that contact duration tracks the slowest vibration frequency) is supported only by the Section 7 benchmark, a three-mass serially connected spring chain with all springs explicitly free of damping (Section 7: 'All springs are free of damping/dissipation of the energy'). In an undamped linear chain with a unilateral spring, repeated re-contact is an expected mathematical consequence: after separation, the masses continue to vibrate with undiminished amplitude, and contact recocurs whenever the end displacement returns to zero. Real flexible cables and branches possess material and aerodynamic damping and are distributed-parameter systems, so the absence of both dissipation and wave dispersion is a severe limitation. The paper offers no sensitivity studies with damping, no comparison against a beam or cable model, and no convergence or numerical-error analysis for the ODE45 results. Thus the claim that soft-contact models are 'problematic' because rebound counts depend on contact stiffness is not established for the systems the paper ultimately targets (brachiating robots grasping vibrating cables). Additionally, the statement that rigid impact-momentum methods are 'impractical' because each rebound requires stopping integration is an implementational critique of a naive event-driven scheme; complementarity-based nonsmooth solvers handle multiple impacts in a single step, so this part of the conclusion is not generally valid. The load-bearing weakness is therefore the unrepresentative undamped lumped model used to justify the broad 'impractical/problematic' verdicts.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper studies impact modeling in multibody systems colliding with deformable structures, with brachiating robots as the motivating application. The first part (Sections 3-4) derives standard impulse-momentum balance equations for frictionless and frictional impacts, expressing post-impact velocity changes in terms of the mass matrix, constraint Jacobians, and a restitution coefficient. The second part presents two numerical studies: a ten-body planar manipulator hitting a rigid obstacle, and a planar system with three unilateral contacts where the endpoint hits a three-mass elastic chain with unilateral springs. The main conclusions, stated in Section 8, claim that classical impact-momentum balance techniques are impractical for impacts with elastic structures because multiple rebounds require repeated interruption of integration, and that soft-contact models are problematic because rebound counts depend on contact stiffness while the total contact duration tracks the slowest vibration frequency of the elastic counterpart.","tokens_in":14700,"tokens_out":3143,"duration_ms":34038,"significance":"The paper's main contributions are the standard rigid-impact formulation with frictional cases and two illustrative numerical examples. The observation in Section 6 that the ratio of elasticities at distant contact points is a significant model parameter is interesting and worth reporting. However, the broad conclusions in Section 8 about the impracticality of rigid methods and the problematic nature of soft-contact models are not supported by the numerical evidence presented. The claims are based entirely on an undamped, three-mass lumped-parameter model without validation, convergence studies, or comparison with state-of-the-art nonsmooth solvers. If the conclusions were supported, they would be useful guidance for modeling brachiation robot interactions with flexible cables; as it stands, the paper does not establish them. The rigid-impact derivation is standard and appears correct, but it is not the load-bearing new content.","major_comments":[{"comment":"The central conclusion that soft-contact models are 'problematic' and that contact duration corresponds mainly to the slowest vibration frequency rests solely on the three-mass undamped spring chain described in Section 7 (Fig. 4d), where 'all springs are free of damping/dissipation of the energy.' In an undamped linear chain with a unilateral spring, repeated re-contact is an expected mathematical consequence: after separation, the masses vibrate with undiminished amplitude, and re-contact occurs when the end displacement returns to zero. Real flexible cables and branches possess material and aerodynamic damping and are distributed-parameter systems. Without sensitivity studies with damping or comparison against a beam or cable model, the claim that rebound counts are sensitive to contact stiffness in a way that is problematic is not established for the systems that the paper ultimately targets (brachiating robots grasping vibrating cables). This is a load-bearing issue for the paper's main conclusion.","section":"Section 7 and Section 8"},{"comment":"The statement that classical unilateral constraint models and impact-momentum balance techniques are 'impractical' because each rebound demands stopping the numerical integration is an implementational critique of a naive event-driven scheme. Complementarity-based nonsmooth solvers, such as those of Moreau and Glocker-Pfeiffer (references [13], [28], and [29] in the paper), handle multiple simultaneous or successive impacts within a single time step without stopping the integration. The paper does not compare its event-driven approach with such methods, so the broad claim of impracticality is an opinion rather than a result established by the manuscript's own analysis. This is load-bearing for the recommendation against rigid methods.","section":"Section 8"},{"comment":"The numerical studies lack validation, convergence analysis, and error bounds. The only numerical details given are the use of MATLAB's ODE45 with maximal and initial time steps of 10^-4 s and relative/absolute tolerances of 10^-4 and 10^-6. There is no mesh-convergence study, no benchmark against an analytical or high-fidelity solution, and no assessment of how the discrete rebound counts shown in Fig. 8 depend on the integration tolerances or time steps. Since the paper reports a specific number of rebounds (up to 9) and claims that the total contact duration is nearly independent of stiffness, convergence evidence is necessary to distinguish physical behavior from numerical artifacts.","section":"Sections 6-7"},{"comment":"The soft-contact model used in Section 6 is not fully specified. The paper refers to a 'smoothed contact model (elastic contact area)' but does not give the constitutive relation for the contact force (e.g., linear spring, Hertzian, with or without damping), the exact definition of penetration, or how the unilateral constraints at points A, B, and C are enforced and smoothed. The parameters c1A, c2A, c3A are stated, but the functional form of the contact force is absent. This makes the numerical results irreproducible and prevents the reader from assessing whether the observed behaviors are artifacts of the particular regularization.","section":"Section 6"}],"minor_comments":[{"comment":"There are two equations labeled (5): the modified dynamic equation and its integrated form; subsequent equation numbers (6)-(12) are shifted accordingly. This numbering error makes the derivation harder to follow.","section":"Section 3"},{"comment":"The text in Eq. (13) says 'Eqs. (13) contain four unknown' but only two equations are displayed; the logical flow of the case distinction for slip and stick is dense and would benefit from a table or explicit step-by-step summary.","section":"Section 4"},{"comment":"Fig. 8 caption uses c14 in some labels while the text uses cref for the reference stiffness; the caption also does not directly state which subfigure corresponds to which stiffness ratio, and the claimed rebound counts (e.g., 9 rebounds) are not evident from the plotted curves. A table listing stiffness, number of rebounds, and total contact duration would greatly improve clarity.","section":"Section 7"},{"comment":"There are several typographical errors that should be corrected: 'locomoion' in the Fig. 1 caption, 'Culomb' in Section 4, 'vetrices' in Section 2, and the moment of inertia for body #4 is consistently labeled I3 instead of I4 in Section 6.","section":"Throughout"},{"comment":"The claim that 'the overall motion of the multibody part appears to be not influenced (or slightly influenced) by assumed values of the connecting elasticity' is presented without quantitative support; providing a plot of, for example, the arm's final angle or velocity versus c13 would make the claim verifiable.","section":"Section 8"}],"recommendation":"major_revision","confidential_remarks":"The paper's core impulse-momentum derivation is standard, and the multi-contact example in Section 6 has some useful observations, but the broad conclusions in Section 8 overreach the evidence. The author may also want to position the work more carefully relative to the large body of literature on nonsmooth dynamics; the current dismissal of rigid contact methods appears to overlook complementarity-based approaches that do not require stopping integration. The heavy reliance on the author's own previous formulation [50] is not circular, but it would be good to clarify what is genuinely new in this manuscript beyond the two numerical examples."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Short version: the paper is a careful but narrow numerical case study of multi-contact impacts with elastic supports. It applies standard impulse-momentum and soft-contact models to a specific configuration: a multibody system with multiple unilateral contacts and an elastic counterpart made of a three-mass spring chain. The derivations in Sections 3-4 are standard but competently organized, and the handling of slip-stick transitions in frictional impacts is clearly laid out. Section 6 makes a legitimate practical point: in multi-contact systems, the stiffness ratio at distant contact points matters, and co-impact can occur elsewhere. Section 7's classification of mass regimes (backward, backward+, forward) is a useful descriptive taxonomy. The soft spots are where the conclusions overreach. The central claim in Section 8 that soft-contact models are 'problematic' rests entirely on the Section 7 benchmark, where every spring is explicitly free of damping. In an undamped linear chain, repeated re-contact after separation is expected, not a surprise. Real cables and branches have damping and are distributed systems, so the rebound-count sensitivity and the duration-frequency relationship are not established for the systems the paper targets. The other broad claim, that impulse-momentum methods are impractical because each rebound requires stopping integration, applies to naive event-driven schemes; complementarity-based solvers handle multiple impacts in one step, so that statement is too general. There is no code or data, and the soft-contact force law is not fully specified, so independent reproduction is not possible. None of this is fatal to the paper as a bounded case study. The fix is revision: add damping sensitivity, compare with a distributed model, ship the code, and soften the conclusions to match what was actually computed. This paper is for practitioners modeling brachiation or elastic-support impacts. It deserves a serious referee because the numerical observations could influence modeling choices, but the referee should press for validation and more cautious framing. My recommendation: send to peer review with expectations of major revision, not desk reject.","headline":"A careful but narrow numerical case study of multi-contact impacts with elastic supports; the standard methods are clearly presented, but the broad conclusions in Section 8 overreach what the undamped three-mass simulations actually support.","tokens_in":767,"tokens_out":1600,"would_cite":false,"duration_ms":37383,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["70E55","70F35"],"pacs":["45.40.-f"],"model":"deepseek-v4-flash","headline":"When a multibody system strikes an elastic structure, standard rigid impact models become impractical and soft-contact models give rebound counts that depend on the arbitrarily chosen contact stiffness.","keywords":["impact modelling","multibody dynamics","unilateral constraints","soft contact models","deformable structures","impulse-momentum balance","brachiation robots","elastic collisions"],"falsifier":"Perform an instrumented collision between a rigid arm and a real cable or beam, varying either the contact stiffness at the gripper or the structural damping, and count the distinct rebounds and measure the total contact duration; the paper's claim fails if contact duration does not track the slowest vibration frequency, if rebound count does not grow with contact stiffness, or if modest damping removes the multi-rebound sequence.","tokens_in":14217,"feed_emoji":"⚙️","tokens_out":8793,"duration_ms":85614,"temperature":0.7,"pith_summary":"This paper tackles a practical modeling problem: a multibody mechanism, motivated by brachiation robots swinging between branches, collides with an elastic structure such as a vibrating cable, and the collision turns into a train of rebounds rather than one clean impact. The author argues that the two standard approaches both fail here: classical rigid-body impulse-momentum balance requires stopping and restarting the numerical integration at every rebound, which quickly becomes impractical, and soft-contact models yield a count of rebounds that depends strongly on the chosen contact spring stiffness, even though the gross motion of the multibody part is nearly unaffected. The duration of the contact episode instead tracks the slowest vibration frequency of the elastic counterpart. If this is right, engineers modeling impacts on flexible structures should not trust either idealization, and simulation effort should go into resolving the low-frequency vibration of the target structure rather than fine-tuning the contact law.","feed_headline":"Rigid impact models fail on flexible structures","feed_subtitle":"Repeated rebounds dominate; contact time tracks the slowest cable mode, not stiffness.","key_machinery":"The load-bearing object is a lumped three-mass chain connected by springs, used as the deformable reference, with the contact itself modeled as a unilateral linear spring that transmits only compressive forces and has no damping; the multibody side is formulated in joint coordinates with Newton/Euler dynamics, and impact impulses are mapped to joint-velocity changes through the mass matrix and a contact-point Jacobian in equations (5)-(12). By varying the unilateral spring's stiffness and the chain masses, the model generates the multi-rebound sequences and shows that contact duration is set by the chain's slowest vibration mode rather than by the contact stiffness. A second, simpler system with two rigid bodies and three unilateral contact points demonstrates why impulse-momentum balancing becomes ambiguous when several unilateral constraints are active at once.","core_discovery":"On the paper's own terms, the central discovery is that impacts with deformable structures are inherently multi-event. In numerical experiments with a three-mass undamped spring chain as the elastic target and a unilateral spring at the contact, the colliding arm shows up to nine rebounds during one contact episode, with the rebound count rising as contact stiffness is increased by factors of 2, 4, 10, and 100 over the reference value, while the total in-touch time stays nearly the same and mainly matches the slowest frequency of the elastic counterpart. The overall motion of the multibody part, such as the arm endpoint displacement and the velocity of the main body, is only weakly dependent on the assumed contact stiffness. From these observations the paper concludes that classic unilateral constraint models and impact-momentum balance techniques are impractical for such cases, and soft-contact models are problematic because their rebound counts are parameter-sensitive.","pith_inferences":["Untested by the paper: adding even mild damping to the chain would likely reduce the rebound count, so the many-rebound prediction may overstate what happens with real cables, which dissipate energy.","If the global-motion insensitivity holds, grasp-timing control could ignore uncertain contact stiffness and rely on a low-order model of the structure's slowest mode.","Impulse-momentum methods might be rescued by merging closely spaced rebounds into one effective impact with an energy-based restitution coefficient, avoiding repeated event stops.","The contact-duration/frequency relation suggests that measuring a structure's fundamental mode from a free-vibration test could calibrate impact timing without resolving the detailed contact force law."],"forward_implications":["Designers of brachiation or cable-inspection robots should expect a collision with a flexible cable to produce several rebounds, not one clean impact event.","Simulation algorithms based on rigid impact events will need one stop-and-restart per rebound, making them costly or impractical when the target is elastic.","Soft-contact simulations should treat rebound count as a parameter-sensitive output, not a reliable prediction; the stable outputs are total contact duration and gross multibody motion.","Contact duration can be predicted from the slowest vibration frequency of the elastic counterpart, offering a cheaper modeling target than the local contact law.","Larger contact stiffness mainly increases the number of rebounds, so increasing stiffness in a soft-contact model does not make the impact more accurate in terms of overall motion."],"supporting_citations":[{"why":"Establishes the two dominant impact modeling alternatives, impulse/momentum balance and constitutive soft contact, that the paper examines.","marker":"[6]"},{"why":"Supplies the claim that impulse-momentum balance cannot be applied straightforwardly when several unilateral constraints are active.","marker":"[9]"},{"why":"Documents the standard assumption that energy converted into post-impact vibrations is negligible, which the paper challenges.","marker":"[10]"},{"why":"Presents penalty/soft-contact models with parameterized penalty functions whose stiffness-dependence the paper probes.","marker":"[44]"},{"why":"Reviews continuous contact-force models, giving the soft-contact approach the paper finds problematic.","marker":"[48]"},{"why":"Provides the joint-coordinate multibody formalism and the impulse-balance equations used for the rigid-impact analysis.","marker":"[50]"}],"fun_headline_variants":["Up to nine rebounds per impact on flexible structures","Contact time tracks structure's slowest mode, not stiffness","Soft-contact models fail due to parameter-sensitive rebound counts","Rigid impact models impractical for flexible targets, paper shows","Rebound count varies with stiffness, contact time does not"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The argument relies on the undamped three-mass spring chain with a unilateral linear spring being a faithful enough model of a real flexible cable or branch; in a real structure, energy dissipation could change both the number and timing of rebounds.","fun_headline_variants_meta":{"raw":{"variants":["Up to nine rebounds per impact on flexible structures","Contact time tracks structure's slowest mode, not stiffness","Soft-contact models fail due to parameter-sensitive rebound counts","Rigid impact models impractical for flexible targets, paper shows","Rebound count varies with stiffness, contact time does not"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000735,"raw_usage":{"total_tokens":3207,"prompt_tokens":786,"completion_tokens":2421,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":402,"completion_tokens_details":{"reasoning_tokens":2342}},"tokens_in":402,"tokens_out":2421,"duration_ms":16939,"temperature":1.0,"reasoning_tokens":2342,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-07T04:53:31.593483+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Perform an instrumented collision between a rigid arm and a real cable or beam, varying either the contact stiffness at the gripper or the structural damping, and count the distinct rebounds and measure the total contact duration; the paper's claim fails if contact duration does not track the slowest vibration frequency, if rebound count does not grow with contact stiffness, or if modest damping removes the multi-rebound sequence.","supporting_citations":[{"cited_title":"G.: Applications of unilateral multibody dynamics","cited_arxiv_id":null,"evidence_quote":"Establishes the two dominant impact modeling alternatives, impulse/momentum balance and constitutive soft contact, that the paper examines."},{"cited_title":"In: The 5th Joint International Conference on Multibody System Dynamics, Liznona: IDMEC - Instituto Superior Técnico, University of Lisbon, pp.1-17 (2108)","cited_arxiv_id":null,"evidence_quote":"Supplies the claim that impulse-momentum balance cannot be applied straightforwardly when several unilateral constraints are active."},{"cited_title":"A.: Modeling of Impact in Multibody Systems: An Overview","cited_arxiv_id":null,"evidence_quote":"Documents the standard assumption that energy converted into post-impact vibrations is negligible, which the paper challenges."},{"cited_title":"Multibody Syst","cited_arxiv_id":null,"evidence_quote":"Presents penalty/soft-contact models with parameterized penalty functions whose stiffness-dependence the paper probes."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Reviews continuous contact-force models, giving the soft-contact approach the paper finds problematic."},{"cited_title":"Wydawnictwo Politechniki Gdańskiej, Seria Monografie 123, Gdańsk (2012) (in Polish)","cited_arxiv_id":null,"evidence_quote":"Provides the joint-coordinate multibody formalism and the impulse-balance equations used for the rigid-impact analysis."}],"review_version":1}